All praise and thanks are due to Allah, and peace and blessings be upon His Messenger.

Dear questioner, may Allah bless your efforts in pursuit of knowledge and enlighten your heart with ikhlas (sincerity)!

In fact, the first ten days of Dhul-Hijjah represent an annual chance, in which a faithful servant of Allah is to bring himself nearer to Him, Most High. These are days of worship, Hajj, charity, peace, sacrifice, and good deeds.

Shedding more light on this issue, we'd like to cite the following Fatwa issued by Sheikh M. S. Al-Munajjid, a prominent Saudi Islamic lecturer and author:

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, in a sense that rewards are multiplied many times than the case in other periods of time. This reflects Allah’s overflowing mercy towards His servants, and it encourages them to do more righteous deeds and makes them more eager to worship Him, so that the Muslim renews his efforts to gain a greater share of reward, prepare himself for death and supply himself in readiness for the Day of Judgment.

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. Everyone of these special occasions involves some kind of worship through which the servants may draw closer to Allah, and some kind of blessing through which Allah bestows His favor and mercy upon whomsoever He wills. Happiness and success are for the one who makes the most of these special months, days and hours and draws nearer to his Lord during these times through acts of worship and righteousness. 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. Almighty Allah says, (And worship your Lord until there comes unto you the certainty.) (Al-Hijr 15: 99) The scholars say: ‘The certainty’ means death.

Among the special seasons of worship are the first ten days of Dhul-Hijjah, which Allah has preferred over all the other days of the year. Ibn `Abbas (may Allah be pleased with him and his father) reported that the Prophet (peace and blessings be upon him) said: "There are no days in which righteous deeds are more beloved to Allah than these ten days." The people asked, "Not even Jihad for the sake of Allah?" He said, "Not even Jihad for the sake 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." (Reported by Al-Bukhari)

Ibn `Abbas (may Allah be pleased with him and his father) also reported that the Prophet (peace and blessings be upon him) said: "There is no deed more precious in the sight of Allah, nor greater in reward, than a good deed done during the ten days of Sacrifice." He was asked, "Not even Jihad for the sake of Allah?" He said, "Not even Jihad for the sake 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." (Reported by Ad-Darimi)

These texts and others indicate that these ten days are better than all the other days of the year, with no exceptions, not even the last ten days of Ramadan. But the last ten nights of Ramadan are better, because they include Laylat al-Qadr, which is better than a thousand months. Thus the various reports may be reconciled. (See TafsirIbn Kathir, 5/412)

You should know, dear questioner, that the virtue of these ten days is based on many things:

1- Allah swears an oath by them, and swearing an oath by something is indicative of its importance and great benefit. Almighty Allah says: (By the dawn; by the ten nights.) (Al-Fajr 89: 1-2) Ibn `Abbas, Ibn Az-Zubayr, Mujahid and others of the earlier and later generations are of the opinion that this refers to the first ten days of Dhul-Hijjah. Ibn Kathir said: "This is the correct opinion." (TafsirIbn Kathir, 8/413)

2- The Prophet (peace and blessings be upon him) testified that these are the best days of this world, as we have already quoted above from authentic hadiths.

3- The Prophet (peace and blessings be upon him) 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.

4- The Prophet (peace and blessings be upon him) commanded us to recite during this time a lot of tasbih (glorification of Allah), as well as tahmid (praising Allah) and takbir (saying 'Allah is Greatest').
`Abdullah ibn `Umar (may Allah be pleased with him and his father) reported that the Prophet (peace and blessings be upon him) said: "There are no days greater in the sight of Allah and in which righteous deeds are more beloved to Him than these ten days, so during this time recite a great deal of tahlil (saying: 'there is no god but Allah'), takbir and tahmid." (Reported by Ahmad)

5- These ten 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 Hajj, which combines acts of worship in a way unlike any other day.

6- These ten days include the days of Hajj.

Excerpted, with slight modifications, from: www.islam-qa.com