The Afikomen is a piece of matzah that is traditionally hidden during the Passover seder.
Breaking the Matzah and Hiding the Afikomen
There are three pieces of matzah used during a Passover seder. During the fourth part of the Seder (called Yachatz) the leader will break the middle of these three pieces in two. The smaller piece is returned to the Seder table and the larger piece is set aside in a napkin or bag. This larger piece is called the "afikomen," a word that comes from the Greek word for "dessert." It is so called not because it is sweet, but because it is the last item of food eaten at the Seder.
Traditionally, after the afikomen is broken, it is hidden. Depending on the family, either the Seder leader hides the afikomen during the meal or the children at the table "steal" the afikomen and hide it. Either way, the Seder cannot be concluded until the afikomen is found and returned to the table so each guest can eat a piece of it. If the Seder leader hid the afikomen the children at the table must search for it and bring it back. They receive a reward (usually candy, money, or a small gift) when they bring it back to the table. Likewise, if the children "stole" the afikomen the Seder leader ransoms it back from them with a reward so that the Seder can continue.
The practice of hiding the afikomen was instituted during the Middle Ages by Jewish families to make the Seder more entertaining and exciting for children (who can become antsy when sitting through a long ritual meal).
Concluding the Seder
Once the afikomen is retuned, each guest receives a small portion at least the size of an olive. This is done after the meal and normal deserts are eaten so that the last taste of the meal is matzah. After the afikomen is eaten the Birkat Ha Mazon (Grace After Meals) is recited and the Seder is concluded.