Praise be to Allah Who has created time and has made some times better than others, some months and days and nights better than others, when rewards are multiplied many times, as a mercy towards His slaves. This encourages them to do more righteous deeds and makes them more eager to worship Him.
This season of worship brings many benefits, such as the opportunity to correct one’s faults and make up for any shortcomings or anything that one might have missed. Each of these special occasions involves some kind of worship through which people may draw closer to Allah, and some kind of blessing through which Allah bestows His favour and mercy upon whomsoever He, Almighty, Wills.
The Muslim must understand the value of his life, increase his worship of Allah and persist in doing good deeds until the moment of death. Allah Almighty says (what means): “And worship your Lord until there comes to you the certainty (death).” [Qur’an 15:99] The commentators said: “The ‘certainty’ means death.” 
Among the special seasons of worship are the first 10 days of Dhul-Hijjah, which Allah has preferred over all the other days of the year. Ibn ‘Abbaas, may Allah be pleased with him, reported that the Prophet, sallallaahu ‘alaihi wa sallam, said: “There are no days in which righteous deeds are more beloved to Allah than these 10 days.” The people (the Companions, may Allah be pleased with them) asked: “O Messenger of Allah, not even Jihad in the path of Allah?” He, sallallaahu ‘alaihi wa sallam, said: “Not even Jihad in the path of Allah, except in the case of a man who went out to fight giving himself and his wealth up for the cause, and came back with nothing (lost both his property and life).” [Al-Bukhari]
This text and others indicate that these 10 days are better than all the other days of the year, with no exceptions, not even the last 10 days of Ramadan. But the last 10 nights of Ramadan are better, because they include the Night of Al-Qadr (Decree), which is better than a thousand months. Thus the various reports may be reconciled. [See Tafseer Ibn Katheer, 5/412]

The virtues of these 10 days:
The virtues are based on many things:
1.    Allah Swears an oath by 10 days of Dhul-Hijjah, and swearing an oath by something is indicative of its importance and great benefit. Allah says (what means): “By the dawn and by the 10 nights (i.e. the first 10 days of the month of Dhul-Hijjah)…” [Qur’an 89: 1-2]
Ibn ‘Abbaas, Ibn Az-Zubayr, Mujaahid and others of the earlier and later generations, may Allah have mercy upon them, said that this refers to the first 10 days of Dhul-Hijjah. Ibn Katheer, may Allah have mercy upon him, said: “This is the correct opinion.” [Tafseer Ibn Katheer, 8/413]
2.    The Prophet, sallallaahu ‘alaihi wa sallam, encouraged people to do righteous deeds because of the virtue of this season for people throughout the world, and also because of the virtue of the place - for the pilgrims to the Sacred House of Allah.
3.    The Prophet, sallallaahu ‘alaihi wa sallam, commanded us to recite a lot of Tasbeeh (“SubhaanAllah”), Tahmeed (“Al-hamdu Lillaah”) and Takbeer (“Allahu Akbar”) during this time. ‘Abdullaah Ibn ‘Umar, may Allah be pleased with him, reported that the Prophet, sallallaahu ‘alaihi wa sallam, said: “There are no days greater in the sight of Allah and in which righteous deeds are more beloved to Him than these 10 days, so during this time recite a great deal of Tahleel (“Laa ilaaha illAllah”), Takbeer and Tahmeed.” [Ahmad]
4.    These 10 days include the Day of ‘Arafah, on which Allah perfected His Religion. Fasting on this day will expiate for the sins of two years. These days also include the Day of Sacrifice, the greatest day of the entire year and the greatest day of Haj, which combines acts of worship in a way unlike any other day. 

Shall you offer a sacrifice?
The Sunnah indicates that the one who wants to offer a sacrifice must stop cutting his hair and nails and removing anything from his skin, from the beginning of the 10 days until after he has offered his sacrifice, because the Prophet, sallallaahu ‘alaihi wa sallam, said: “When you see the new moon of Dhul-Hijjah, if any one of you wants to offer a sacrifice, then he should stop cutting his hair and nails until he has offered his sacrifice.” According to another report he, sallallaahu ‘alaihi wa sallam, said: “He should not remove (literally, touch) anything from his hair or skin.” [Muslim]
The Prophet’s, sallallaahu ‘alaihi wa sallam, instruction here makes one thing obligatory and his prohibition makes another Haraam (prohibited), according to the soundest opinion, because these commands and prohibitions are unconditional and unavoidable. 
However, if a person does any of these things deliberately, he must seek Allah’s forgiveness but is not required to offer (an extra) sacrifice in expiation; his sacrifice will be acceptable. Whoever needs to remove some hair, nails, etc. because it is harming him, such as having a broken nail or a wound in a site where there is hair, can do so, and there is nothing wrong with that. The state of Ihraam is so important that it is permitted to cut one’s hair if leaving it will cause harm. There is nothing wrong with men or women washing their heads during the first ten days of Dhul-Hijjah, because the Prophet, sallallaahu ‘alaihi wa sallam, only forbade cutting the hair, not washing it.
The wisdom behind this prohibition of the one who wants to offer a sacrifice from cutting his hair, etc., is so that he may resemble those in Ihraam in some aspects of the rituals performed, and so that he may draw closer to Allah by offering the sacrifice. So he leaves his hair and nails alone until the time when he has offered his sacrifice, in the hope that Allah will save him in his entirety from the Fire. And Allah knows best.
If a person has cut his hair or nails during the first ten days of Dhul-Hijjah because he was not planning to offer a sacrifice, then he decides later, during the 10 days, to offer a sacrifice, then he must refrain from cutting his hair and nails from the moment he makes this decision.
Some women may delegate their brothers or sons to make the sacrifice on their behalf, then cut their hair during these 10 days. This is not correct, because the ruling applies to the one who is offering the sacrifice, whether or not he (or she) delegates someone else to carry out the actual deed. The prohibition does not apply to the person delegated, only to the person who is making the sacrifice, as is indicated in the narration. The person who is sacrificing on behalf of someone else, for whatever reason, does not have to adhere to this prohibition. 
This prohibition appears to apply only to the one who is offering the sacrifice, not to his wife and children, unless any of them is offering a sacrifice in his or her own right, because the Prophet, sallallaahu ‘alaihi wa sallam, used to sacrifice “on behalf of the family of Muhammad,” but there are no reports that say he, sallallaahu ‘alaihi wa sallam, forbade them to cut their hair or nails at that time.
If a person was planning to offer a sacrifice, then he decides to go and perform Hajj, he should not cut his hair or nails if he wants to enter ihraam, because the Sunnah is only to cut hair and nails when necessary. But if he is performing Tamattu’ [whereby he performs ‘Umrah, comes out of ihraam and enters ihraam anew for Haj], he should trim his hair at the end of his ‘Umrah because this is part of the ritual.

Types of worship and deeds to be performed during the 10 days

One must understand that these days are a great blessing from Allah to His slave, which is appreciated properly by the actively righteous. It is the Muslim’s duty to appreciate this blessing and make the most of the opportunity, by devoting these ten days to paying more attention to striving hard in worship.
Among His blessings to His slaves, Allah has given us many ways in which to perform righteous deeds and worship Him, so that the Muslim may be constantly active and consistent in his worship of his Lord.
Among the righteous deeds which the Muslim should strive to perform during the first 10 days of Dhul-Hijjah are:
1.    The performance of Haj and ‘Umrah, which are the best of deeds that may be done. And what indicates their superiority are a number of narrations, one of which is the saying of the Prophet, sallallaahu ‘alaihi wa sallam: “Performance of ‘Umrah is an expiation of the sins committed between it and the previous ‘Umrah, and the reward of the Haj which is accepted by Allah, Most High, is nothing but Paradise.” [Al-Bukhari and Muslim]
2.    Fasting: It is recommended to fast on the nine days and especially on the ninth day of Dhul-Hijjah. There is no doubt that the act of fasting is one of the best deeds, and it is from what Allah, Most High, has chosen for himself, as in the Sacred Hadith: “Fasting is for Me (Allah), and it is I who give reward for it. Verily, someone gives up his sexual passion, his food and his drink for my sake...” [Al-Bukhari, Muslim, At-Tirmithi, An-Nasaa’i and Ibn Maajah]
Also, from Abu Sa’eed al-Khudri, may Allah be pleased with him, who said that the Messenger of Allaah, sallallaahu ‘alaihi wa sallam, said: “No servant (of Allah, Most High) fasts one day in the way of Allah, except that Allah, the Most High, removes his face from the fire because of it (the distance of traveling) seventy years.” [Al-Bukhari and Muslim]
The Prophet, sallallaahu ‘alaihi wa sallam, said: “Fasting the Day of ‘Arafah will be credited with Allah by forgiving one’s sins of the previous year and the following year.” [Muslim]
3.    Uttering the mention of Allah: It is recommended to utter Takbeer (“Allaahu Akbar”), Tahmeed (“Al-hamdu Lillaah”), Tahleel (“La ilaaha illallaah”) and Tasbeeh (“Subhaanallaah”) during the first ten days of Dhul-Hijjah in the Mosque, at home, on the street and every place where it is permitted to mention Allah and mention His name out loud, as an act of worship and as a proclamation of the greatness of Allah, Most High. He The Most High, says (what means): “...And mention the name of Allah on known [i.e., specific] days...” [Qur’an 22: 28]
4.    Performing more good deeds in general, because good deeds are beloved by Allah and will bring a great reward from Him. Whoever is not able to go to Hajj should occupy himself at this blessed time by worshipping Allah, praying, reading Qur’an, supplicating, giving charity, honouring his parents, upholding the ties of kinship, enjoining what is good and forbidding what is evil, and other good deeds and acts of worship.
5.  Offering sacrifice. One of the good deeds that will bring a person closer to Allah during these 10 days is offering a sacrifice, by choosing a high-quality animal. It is the Sunnah of our father Ibraaheem, may Allah exalt his mention - from when Allah The Most High, redeemed his son by the great sacrifice (of an animal in his place). The Prophet, sallallaahu ‘alaihi wa sallam, slaughtered (sacrificed) two horned rams, black and white in colour, and he, sallallaahu ‘alaihi wa sallam, slaughtered them with his own hands, mentioned the name of Allah (saying Bismillaah), said Takbeer (Allaahu-Akbar), and placed his foot on their sides (while slaughtering them). [Al-Bukhari and Muslim]
6.    Sincerely repenting. One of the most important things to do during these 10 days is to repent sincerely to Allah and to give up all kinds of disobedience and sin.
Repentance means coming back to Allah and foregoing all the deeds, open and secret, that He dislikes, out of regret for what has passed, giving it up immediately and being determined never to return to it, and to adhere firmly to the Truth by doing what Allah loves. The Prophet, sallallaahu ‘alaihi wa sallam, said: “Verily Allah has a sense of ‘Ghayrah’ (honour, prestige and anger over violation), and Allah’s sense of Ghayrah is provoked when a person does that which Allah has made prohibited.” [Al-Bukhari and Muslim]
7.    It is incumbent for the Muslim (who is not making Haj) to make every effort to perform the ‘Eid Prayer wherever it is performed, and to be present for the Khutbah (sermon) and benefit. 
He must know the wisdom behind the legislation of this ‘Eid (celebration). It is a day of thankfulness and performing deeds of righteousness. So, he must not make it a day of wildness, pride and vanity. He should not make it a time of disobedience and increase in forbidden things such as music, singing, uncontrolled amusement and the like - those things which could cause the cancellation of the good deeds done in these 10 days (of Dhul-Hijjah).
There is much to be gained, so make the most of the opportunity afforded by these invaluable and irreplaceable ten days. Hasten to do good deeds, before death strikes, before one regrets his negligence and failure to act, before one is asked to return to life but only when prayers will never be answered, before death intervenes between the hopeful one and the things he hopes for, before one is trapped with his deeds in the grave. (Taken from Al Jumu’ah magazine)
Article source: http://www.islamweb.net/emainpage/