Eid al-Adha is the biggest festival of muslims. It also called "Sacrifice Feast" or "Festival of the Sacrifice". At the time of Hajj Muslims remember and celebrate the trials and victory of the Prophet Ibrahim by themselves killing an animal such as a goat, sheep or camel.
The main reason for celebrating is to celebrate the spirit of following the commands of God the same way prophet Ibrahim and his son Ismail has done. When Ibrahim went Mecca with his wife and son, Mecca was a desolate and barren desert and Ibrahim had to face a lot of hardships at that time, however he fulfilled the Allah will without any reason. In a divine dream, he was ready to sacrifice his son for Allah's sake. He was completely ready to give up his life for God But miraculously enough, when Ibrahim was about to sacrifice son, Allah save the boy's life and replaced him with a lamb. And this is what Ibrahim ultimately sacrificed.
To celebrate this belief act of sacrifice by Prophet Ibrahim, On Eid-ul-Adha people slaughter a lamb, goat, ram or any other animal and One-third is distribute in immediate family and relatives, one-third is given away to friends, and one-third is donated to the poor.
Sacrificing an animal is just a physical form but the actual learning is to remind everyone that how one needs to be ready to follow the commands of Allah SWT. As its clearly mentioned in another place in Quran.
These two verses of Quran give a clear idea of what Eid ul Adha is and why Muslims practice it, though most of them just enjoy having delicious food and get into the discussions of cow, buffalo, a bull or a sheep sacrifices.