Ibn' Abbas says about the Aayah, "Remember Allah during the well known days," it refers to the first ten days of Dhul-Hijjah. [This is related by al-Bukhari]

Allah swears an oath by them, and swearing an oath by something is indicative of its importance and great benefit. Allah says (interpretation of the meaning), "By the dawn; by the ten nights" [al-Fajr 89:1-2]. Ibn Abbaas, Ibn al-Zubayr, Mujaahid, and others of the earlier and later generations said this refers to the first ten days of Dhul-Hijjah. Ibn Katheer said: "This is the correct opinion." [Tafseer Ibn Katheer, 8/413]

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 the believers. This encourages them to do more righteous deeds and makes them more eager to worship Him, so that the believer renews his efforts to gain a greater share of reward, prepare himself for death and supply himself in readiness for the Day of Judgement.

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. Every one of these special occasions involves different acts of worship through which believers may draw closer to Allah and through these acts of worship, Allah bestows His favor and mercy upon whomsoever He will. The successful person is 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; he will most likely be touched by the blessing of Allah and will feel the joy of knowing that he is safe from the flames of Hell. [Ibn Rajab, al-Lataaif, p.8]

Ibn'Abbas reports that the Messenger of Allah ﷺ said, "No good deeds done on other days are superior to those done on these days [meaning the ten days of Dhul-Hijjah]." The companions asked, "O Messenger of Allaah, not even jihad in the way of Allaah?" He said, "Not even jihad, except for the man who puts his life and wealth in danger [for Allaah's sake] and returns with neither of them." [Related by the Muslim and an-Nasa'i]

Ahmad and at-Tabarani record from Ibn Umar that the Messenger of Allah ﷺ said, "There is no day more honorable in Allaah's sight and no acts more beloved therein to Allaah than those in these ten days. So say tahlil (There is no deity worthy of worship but Allaah : Laa ilaaha illallaah), takbir (Allaah is the greatest Allaahu Akbar) and tahmid (All praise is due to Allaah : alhumdulillaah) a lot [on those days]." [Reported by Ahmad, 7/224; Ahmad Shaakir stated it is saheeh]

Abu Hurairah relates that the Messenger of Allah ﷺ said, "There are no days more loved to Allah for you to worship Him therein than the ten days of Dhul Hijja. Fasting any day during it is equivalent to fasting one year and to offer salatul tahajjud (late-night prayer) during one of its nights is like performing the late-night prayer on the night of power. [i.e., Lailatul Qadr]." [This is related by at-Tirmidhi, Ibn Majah, and al-Baihaqi]

Ibn' Umar narrated that at Mina, the Messenger of Allah ﷺ said, "Do you know what is the day today?" The people replied, "Allah and His Messenger know it better." He said, "It is the forbidden (sacred) day. And do you know what town is this?" They replied, "Allah and His Messenger know it better." He said, "This is the forbidden (sacred) town (Mecca). And do you know which month is this?" The people replied, "Allaah and His Apostle know it better." He said, "This is the forbidden (sacred) month." The Messenger added, "No doubt, Allaah made your blood, your properties, and your honor sacred to one another like the sanctity of this day of yours in this month of yours in this town of yours."

Narrated Ibn Umar: On the Day of Nahr (10th of Dhul-Hijja), the Messenger ﷺ stood in between the Jamrat during his Hajj which he performed (as in the previous Hadith) and said, "This is the greatest Day (i.e. 10th of Dhul-Hijjah)." The Messenger started saying repeatedly, "O Allah! Be Witness (I have conveyed Your Message)." He then bade the people farewell. The people said, "(This is Hajjat-al-Wada)." [Bukhari 2.798]

Fasting Day of Arafat

Abu Qatadah reported that the Messenger of Allah ﷺ said, "Fasting on the day of 'Arafah is an expiation for two years, the year preceding it and the year following it. Fasting the day of 'Ashurah is an expiation for the year preceding it." [This is related by "the group," except for al-Bukhari and at-Tirmidhi]

Hafsah reported, "There are five things that the Messenger ﷺ never abandoned: fasting the day of 'Ashurah, fasting the [first] 10 [days of Dhul-Hijjah], fasting three days of every month and praying two rak'ah before the dawn prayer." [This is related by Ahmad and an-Nasa'i]

Uqbah ibn Amr reported that the Messenger of Allah ﷺ said, "The day of 'Arafah, the day of sacrifice, and the days of tashreeq are'ids for us--the people of Islam--and they are days of eating and drinking." [Related by "the five," except for Ibn Majah. At-Tirmidhi grades it sahih]

Abu Hurairah stated, "The Messenger of Allah ﷺ forbade fasting on the day of' Arafah for one who is actually at 'Arafah." [Related by Ahmad, Abu Dawud, an-Nasa'i, and Ibn Majah]

At-Tirmidhi comments: "The scholars prefer that the day of 'Arafah be fasted unless one is actually at 'Arafah."

Takbeer

It is Sunnah to say Takbeer ("Allaahu akbar"), Tahmeed ("Al-hamdu Lillaah"), Tahleel ("La ilaha ill-Allaah") and Tasbeeh ("Subhaan Allaah") during the first ten days of Dhul-Hijjah, and to say it loudly in the mosque, the home, the street and every place where it is permitted to remember Allah and mention His name out loud, as an act of worship and as a proclamation of the greatness of Allah, may He be exalted. Men should recite these phrases out loud, and women should recite them quietly.

Allah says (interpretation of the meaning)

"That they might witness things that are of benefit to them (i.e., the reward of Hajj in the Hereafter, and also some worldly gain from trade, etc.), and mention the name of Allah on appointed days, over the beast of cattle that He has provided for them (for sacrifice)..." [al-Hajj 22:28]

The majority of scholars agree that the "appointed days" are the first ten days of Dhul-Hijjah, because of the words of Ibn Abbas (may Allah be pleased with him and his father), "The appointed days are the first ten days (of Dhul-Hijjah)."

The Takbeer may include the words "Allah akbar, Allaahu akbar, la ilaaha ill-Allah; wa Allaahu akbar wa Lillaahil- hamd (Allah is Most Great, Allah is Most Great, there is no deity worthy of worship but Allah; Allah is Most Great and to Allaah be praise)," as well as other phrases.

Takbeer at this time is an aspect of the Sunnah that has been forgotten, especially during the early part of this period, so much so that one hardly ever hears Takbeer, except from a few people. This Takbeer should be pronounced loudly, in order to revive the Sunnah and as a reminder to the negligent. There is sound evidence that Ibn Umar and Abu Hurairah (may Allah be pleased with them) used to go out in the marketplace during the first ten days of Dhul-Hijjah, reciting Takbeer, and the people would recite Takbeer when they heard them. The idea behind reminding the people to recite Takbeer is that each one should recite it individually, not in unison, as there is no basis in Sharee'ah for doing this.