From the day of ’Arafah (the 9th of Dhul-Hijjah), up until the ’Asr Prayer on the thirteen day, are days in which the takbeeraat (saying Allaahu Akbar) should be said.
Imaam al-Khattaabee (d.456H رحمه الله) said: “The wisdom behind saying the takbeeraat in these days is that in the times of jaahiliyyah (pre-lslaamic ignorance), they used to slaughter for their tawaagheet (false objects of worship). So the takbeeraat were prescribed in order to indicate that the act of slaughtering is directed to Allaah alone, and by mentioning only His – the Mighty and Majestic – Name.” [Fathul-Baaree, (21/586)]
Shaykhul-lslaam Ibn Taymiyyah [رحمه الله] said: “All praise be to Allaah. The most correct saying concerning the takbeer – that which the majority of the Salaf (Pious Predecessors), and the Scholars from the Companions and Imaams were upon – is to begin making the takbeer from Fajr (dawn) on the day of ’Arafah, up until the last day of at-Tashreeq (the thirteenth of Dhul-Hijjah), after every Prayer.”
However, what seems more correct is not to restrict the takbeeraat to being just after every Prayer, as al-Haafidh Ibn Hajr pointed out in Fathul-Baaree, (21/587)]