remember Abraham's trials,
102. And, when he (his son) was old enough to walk with him, he said: "O my son! I have seen in a dream that I am slaughtering you (offer you in sacrifice to Allah), so look what you think!" He said: "O my father! Do that which you are commanded, Insha' Allah (if Allah will), you shall find me of As-Sabirin (the patient ones, etc.)."
103. Then, when they had both submitted themselves (to the Will of Allah), and he had laid him prostrate on his forehead (or on the side of his forehead for slaughtering);
104. And We called out to him: "O Abraham!
105. You have fulfilled the dream (vision)!" Verily! Thus do We reward the Muhsinun (good-doers -
106. Verily, that indeed was a manifest trial
107. And We ransomed him with a great sacrifice
The meat from the sacrifice of Eid al-Adha is mostly given away to others. One-third is eaten by immediate family and relatives, one-third is given away to friends, and one-third is donated to the poor. The act symbolizes our willingness to give up things that are of benefit to us or close to our hearts, in order to follow Allah's commands. It also symbolizes our willingness to give up some of our own bounties, in order to strengthen ties of friendship and help those who are in need. We recognize that all blessings come from Allah, and we should open our hearts and share with others.
It is very important to understand that the sacrifice itself, as practiced by Muslims, has nothing to do with atoning for our sins or using the blood to wash ourselves from sin. This is a misunderstanding by those of previous generations: "It is not their meat nor their blood that reaches Allah; it is your piety that reaches Him." (Qur'an 22:37)