Gluttony is the second homunculus to appear in the series, typically being in the company of Lust. He is a large, simple-minded homunculus whose thoughts rarely stray far from eating. He has powerful jaws, acidic saliva, and can and will eat almost anything. He particularly likes eating people, and the only way he can find enjoyment in a battle is if he believes he can eat his opponent afterwards. A running gag in the manga and anime is asking Lust (or any other Homunculi) if he can eat someone. He apparently prefers girls (as in to eat) and also seems to share a bond with his partner Lust. There is no significant information pertaining to his role in the 2003 anime series. In the manga and 2009 anime series; Gluttony is the sixth Homunculus created by Father...

Spoiler

and the failed product of Father's attempts to create a Gate of Truth. When activating this gate, Gluttony's stomach opens up, revealing a large eye at its center. His ribs spread out to act as a border for the gate, and then double as large extendable teeth. With these teeth Gluttony can consume everything in his eye's field of vision in an instant, which is then transported to a realm within himself. Artifacts from centuries before the start of the series can be found there, indicating Gluttony's age. Gluttony and his philosopher's stone was eaten by Pride when they're battling with Edward Elric, Lan Fan, Ling Yao, Fu,and the chimeras.

(Taken in part from Wikia)