Eid-ul-Adha
Eid-ul-Adha is the celebration of sacrifice, and is important to all muslims for various reasons. Two these are the element of sacrifice, and the Hajj.
The Sacrifice
During Eid-ul-Adha, we remember the spirit of Prophet Ibrahim (peace be upon him) and how he was willing to sacrifice the person he loved the most, because it was Allah's (swt) command.
Allah chose Ibrahim to restore the Kabah from disrepair, and Ibrahim had his son Isma'eel (peace also be upon him) help him. It took them months in the desert heat, but they kept going because of their love for Allah (swt).
Once the Ka'bah was finally done, Allah asked Ibrahim (on the 10th day of the month of Dhul' Hijja - the day we celebrate Eid) to sacrifice Isma'eel.
Prophet Ibrahim (Alaihissalaam) was asked to sacrifice his own son Isma'eel, and Ibrahim didn't even once think "why" or that he might say "no" - if that's what his Lord wanted, he trusted Him no matter what!
His faith was rewarded when his son's life was spared by Allah at the very last minute. A lamb was, by the will of Allah sacrificed, in the place of Isma'eel.
Tha Hajj
Eid-ul-Adha ends the period of Hajj (the 5th pillar of Islam - remember?). Every year, about 3 million people go to Mecca and perform the pilgrimage together.
Everyone is dressed the same, nobody is better than anybody else. Seeing the Kabah is like a homecoming - the place on earth where you can be closest to Allah.
This is the spot you face everyday at home when you do your prayers - and now you're really there! You forget about everything else in the world except what you are doing at that moment. Even the people who do not perform the Hajj that year think about what it symbolizes and celebrate that.
Celebrating Eid-ul-Adha with your family and friends is similar to that of Eid-ul-Fitr. Many people also sacrifice animals (like goats or lambs) for this Eid, which is a sunnah act.
When this is done, 1/3 of the meat goes to the needy people, 1/3 is given to neighbors and friends, and 1/3 stays with your family.