The name Afikomen comes from the Greek word Epicurean which means dessert. The Afikomen takes the place of the Pascal Lamb, which can only be eaten when the Temple is extant, and it is the last thing that can be eaten on the Seder Night. We break the matza to symbolize the fact that we are not able to eat the Pascal Lamb; but we place our trust in God that the Third Temple will be rebuilt and the Mitzvah of the Pascal Lamb will be reinstated.
It must be eaten from the same matza that was used at the beginning of the Seder. The Sefat Emet explains that the matza we eat at the
beginning is Lechem Oni, Poor Man's Bread, to remind us of our enslavement to Pharaoh, after that the matza takes on a new symbolism, that of freedom. At the end of the Seder, after having been redeemed by God, we re-enslave ourselves - this time to God Himself. Therefore it is very appropriate that we eat the half of the same matza that we ate at the very start of the Seder.