Afikoman also called epikomen or epikomion literally means dessert in Hebrew. It is the piece of matzah that is broken in the beginning of the Passover Seder and kept aside to be eater at the end of the meal.

It is a tradition where the head  of the Seder hides the broken piece of matzah and ask the children to find it and in return rewards them with candies and other gifts. In some families the children steal the afikoman kept on the table without the head knowing  and  ask a reward for it. This custom is actually followed for keeping the children awake during the proceedings of the Seder and also to make it entertaining for the children.

Procedure

While performing the fourth part of the Seder called the Yahatz, the matzah is broken into two pieces and the larger piece is wrapped in a napkin and either hidden or left for being stolen by the kids. This piece of the matzah is called the Afikoman. This Afikoman is kept for eating during the step called Tzafun.  The Seder cannot be concluded until the afikoman is fount and returned to the table so that each member can have it. Once the afikoman is returned to the table, each person gets a small piece (atleast the size of an olive).  This is done after the main meal and the desserts so that the last last of the Seder is the matzah. According to the religious law, nothing should be eaten after the the afikomen. 

Significance

The matzah eaten at the beginning of the meal is symbolic of the past and of the deliverance from Egypt. The matzah reserved as the afikoman and eaten at the end of the meal is symbolic of future redemption. The hiding of the afikoman can be said to be symbolic of the hidden nature of the future redemption such as the uncertainty of knowing what will happen tomorrow and how it will come to pass.