Gluttony is derived from the Latin gluttire, meaning "to gulp down or swallow." It is one of the Seven Deadly Sins in Judeo-Christian Theology. It is the over-consumption of food, drink, or intoxicants "to the point of waste." This is the key: "waste." Gluttony is a waste of food, a waste of flesh, a waste of literal waste. So says Enotes criticism:
As Dante ascends Mount Purgatory, he meets in turn souls who have experienced the seven deadly sins: pride, envy, wrath, sloth, avarice, gluttony, and lust...The last three sins are from loving too much and focusing that love on earthly things. Practicing control and balance is stressed throughout Purgatorio. Another theme that predominates is that one should remain focused on Paradise and not become too attached to earthly pursuits.
You may be able to use a modern movie in your introduction as an attention-getter. If you've seen the movie Se7en, Kevin Spacey's character's first murder is "Gluttony" in which he tortures an obese man to eat vats of spaghetti until his insides burst. The sadistic killer even had a bucket for the sinner to vomit in, as the body tried to expel the waste before explosion. Vomit is similar to the excrement.
To me, this is a case of the punishment fitting the crime. Dante has this happen because it is really a fitting punishment for what they did.
By eating too much (and using up things that others could have used), the gluttons created waste. This is both physical waste -- they ate a lot and would have therefore created a lot of feces -- and waste in terms of using up resources unnecessarily.
So it is fitting that they should spend eternity in waste. They are paying for their lives by living in the results of their sin.