Purpose of Eidul Adha or Eid of sacrifice

It has several purposes. First, is it is an Eid or day of lawful enjoyment. Islam has not prescribed many festivals , it has only two.Many nations have many festivals, for instance in India. Islam is practical, does not want to waste time on many festivals.
Second, Eidul Azha is a remembrance of great sacrifice of Ibrahim A.S., his total obedience to Allah. In actuality Allah’s command to him to sacrifice his son Ismail A.S. was only to test him, finally only a sheep was sacrificed.
Third, Eidul Adha connects us with Hajj. When in Arafat, Mina and Makkah, Hajj is being performed by Muslims who have traveled there for Hajj, the Muslims around the world are observing Eidul Adha  with Eid prayer and animal sacrifice ( by those who are solvent).
Sacrifice of a goat or sheep etc is Wajib or obligatory  according to Hanafis but Sunnah (a recommended act) according to majority of jurists ( Ref–Imam Nababi’s commentary of Muslim Sharif)
Sacrificial animal meat is shared with relations and others which adds to the celebration of Eid.
There should not be any show off in this regard as Allah says in Sura Hajj ‘the blood or meat of the animal does not reach Allah, only Taqwa or your piety reaches him’
Shah Abdul Hannan