Gluttony, in the biblical sense, refers to one of the seven deadly sins. It consists on the act of indulging excessively with food, drink, or material things. The idea is that, by over-indulging, we act in maliciously, selfish ways.
Since Doctor Faustus is a man who likes to tamper with the established order of things, and push issues to a deeper level, he would naturally want to indulge in every single one of the seven deadly sins. Since he has made a pact with Mephistophilis he really believes that he is otherwordly and beyond consequences, even in committing the deadly sins. This is shown in Scene VII.
During this scene, Mephistophilis indulges Doctor Faustus to a visit to Rome, for an audience with the Pope. Remember how Faustus really believes that he deserves and is allowed to do everything he wants. This time, he asks the devil to make him invisible during the audience, so that he (Faustus) and the devil would have a good laugh courtesy of the friars and the Pope.
(The entire section contains 567 words.)