The Last Best Day of Dhul Hijjah – Day of Nahr AND The 3 Days of Tashreek are all Days of ‘Eid!
The tenth day of Dhul-Hiijah is known as the day of an-Nahr (slaughtering), since it marks the ending of the major rites of Hajj (Pilgrimage), and commemorates the bounty and mercy of Allaah – the Most High – in that He gave His beloved Prophet Ibraaheem – ’alayhis-salaam – a ram to sacrifice in place of his firstborn son Ismaa’eel – ’alayhis-salaam. And out of the ten best days of the year, it is the day of an-Nahr which is the most excellent day of the year with Allaah.Shaykhul-Islaam Ibn Taymiyyah (d.728H) – rahimahullaah – said,
••►“The most excellent day of the week is the day of Friday, by the agreement of the Scholars. And the most excellent day of the year is the day of an-Nahr. And some of them said that it is the day of ’Arafah. However, the first opinion is the correct one, since it is related in the Sunan collections that the Prophet (sallallaahu ’alayhi wa sallam) said,
••►“The most excellent days with Allaah is the day of an-Nahr, then the day of al-Qarr (the day that the Muslims reside in Minaa).” ” 
The Prophet (sallallaahu ’alayhi wa sallam) said,
••► “The greatest day of the Hajj (Pilgrimage) is the Day of an-Nahr (Slaughtering).” 
The day of an-Nahr is also known as ’Eedul-Adhaa (the Festivity of Sacrifice) and is one of the two major festivals that Allaah has granted to this Ummah. Anas (radiyallaahu ’anhu) said, ‘The Prophet (sallallaahu ’alayhi wa sallam) came to al-Madeenah and the people of al-Madeenah had – since the times of jaahiliyyah(Pre-lslaamic Ignorance) – two days which they marked out for play and amusement. So the Prophet (sallallaahu ’alayhi wa sallam) said,
••► ‘I came to you, and you had two days of play and amusement in the times ofjaahiliyyah. But Allaah has replaced them with something better for you: The day of al-Adhaa (sacrificing) and the day of al-Fitr (ending the Fast).” 
The Prophet (sallallaahu ’alayhi wa sallam) also said,
••►“The day of al-Fitr, and the day of an-Nahr, and the days of at-Tashreeq (the three days after an-Nahr) are four days of ’Eed (festivity); and they are days of eating and drinking.” 
’Eedul-Adhaa, is a day in which the Muslims slaughter a camel, cow, sheep or goat, in commemoration of the sacrifice of Ibraaheem – ’alayis-salaam. And this sacrifice is an obligation upon all those who have the means to do so – according to the most correct opinion of the Scholars.  The basis of this is the Prophet’s (sallallaahu ’alayhi wa sallam) saying,
••►“One who has the ability to sacrifice, but chooses not to do so, should not approach our place of (’Eed) Prayer.”  And his (sallallaahu ’alayhi wa sallam) saying,
••► “Whosoever sacrificed before the Prayer, then let him do so again. But whosoever has not sacrificed, then let him sacrifice.”  So this order refers to those who have the ability to do so – and Allaah knows best.
As regards those who intends to sacrifice – normally the head of the household – then they are prohibited from cutting their hair or nails, starting from the first day of Dhul-Hijjah up until after the sacrifice. Allaah’s Messenger (sallallaahu ’alayhi wa sallam) said,
••► “When the ten days start, and one of you intends to sacrifice, then let him not cut his hair or his nails.” 
GLORIFYING ALLAAH WITH THE TAKBEER:
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) – rahimahullaah – 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.” 
Shaykhul-lslaam Ibn Taymiyyah – rahimahullaah – 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.” 
Ibn Abee Shaybah relates,••► “That ’Ali (radiyallaahu ’anhu) used to make the takbeer beginning after the Fajr Prayer on the day of ’Arafah, up until after the ’Asr Prayer on the last day of at-Tashreeq.” 
As regards the actual wording of the takbeeraat, then nothing authentic has been related from the Prophet (sallallaahu ’alayhi wa sallam). However, certain wordings have been authentically related from a group of Companions. From them: Ibn Mas’ood (radiyallaahu ’anhu) would say,
الله أكبر الله أكبر ، الله أكبر لا إله إلا الله ، والله أكبر الله أكبر ولله الحمد
“Allaah is great, Allaah is great. None has the right to be worshipped except Him. And Allaah is great, Allaah is great. And to Him belongs all praise. ” 
Ibn ’Abbaas (radiyallaahu ’anhu) said, “Allaah is great, Allaah is great, Allaah is great, and to Allaah belongs all praise. Allaah is greater and Sublime. Allaah is greater to what He has guided us to. [Allaahu akbar, Allaahu akbar, Allaahu akbar, wa lillaahil-hamd. Allaahu akbar wa ajalla. Allaahu akbar ’alaa maa hadaanaa.]” 
Unfortunately, many Muslims have neglected the takbeer established from our Salaf (Pious Predecessors) and have instead resorted to additions which have no basis at all.
Al-Haafidh Ibn Hajr (d.856H) – rahimahullaah – said, “Indeed, additions have been invented upon this day, which have no basis at all.” 
And may Allaah have mercy upon the one who said,
“Every good is in following the Salaf; And every evil is in the innovations of the late-comers.”
And all praise is for Allaah, Lord of the worlds. And may Allaah extol and send the choicest blessings of peace upon our Leader, Muhammad, and upon his Family, his Companions, and all those who follow them.
 Refer to Jaami’ut-Tirmidhee (3/377).
 Saheeh: Related by Aboo Daawood (no. 1765), from ’Abdullaah Ibn Qart (radiyallaahu ’anhu). It was authenticated by al-Albaanee in Irwaa‘ul-Ghaleel (no. 2018).
 Refer to Majmoo’ul-Fataawaa (25/288).
 Saheeh: Related by Aboo Daawood (no. 1945), from Ibn ’Umar (radiyallaahu ’anhu). It was authenticated by al-Albaanee inal-lrwaa‘ (no. 1101).
 Saheeh: Related by Ahmad (3/103).it was authenticated by al-Haafidh Ibn Hajr in Bulooghul-Maraam (no. 398).
 Saheeh: Related by Ahmad (no. 1945), from ’Uqbah Ibn ’Aamir (radiyallaahu ’anhu). It was authenticated by al-Albaanee in Saheehul-Jaami’ (no. 8192).
 As explained by Ibn Taymiyyah in Majmoo’ul-Fataawaa (23/162-164).
 Hasan: Related by Ibn Maajah (no. 3123), from Aboo Hurayrah (radiyallaahu ’anhu). It was authenticated by Shaykh al-Albaanee in Takhreej Mushkilatul-Fiqr (no. 398).
 Related by al-Bukhaaree (no. 5562) and Muslim (no. 1960), from Jundub Ibn ’Abdullaah al-Bajalee (radiyallaahu ’anhu).
 Related by Muslim (no. 1977), from Umm Salamah (radiyallaahu ’anhaa).
 Quoted from Fathul-Baaree (21/586).
 Majmoo’ul-Fataawaa (24/220). 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).
 Related by Ibn Abee Shaybah in al-Musannaf (2/1/2). It was authenticated by al-Albaanee in al-lrwaa‘ (31/125).
 Related by Ibn Abee Shaybah with an authentic chain of narration
 Related by al-Bayhaqee (3/315) with an authentic chain of narration.
 Fathul-Baaree (2/536).