Think about Cookie Monster. Now think about Ichabod. Okay, back to Cookie Monster. And…Ichabod. Are they blending together yet? That's because Cookie Monster's ever-hungry black hole of a mouth isn't too different from Ichabod's. Ichabod is almost always shoving his face full of food; and when he's not, he's at least salivating at the thought of it.
We know that this guy loves to eat; he's "a huge feeder" and has "the dilating powers of an anaconda" (1.11). But food isn't the only thing that he consumes. He has an "appetite for the marvelous" or the supernatural and "[n]o tale was too gross or monstrous for his capacious swallow" (1.16). His metaphorical mouth also feeds on the "sweet thoughts and 'sugared suppositions'" of riches and power (1.39). We could keep going, but you get the picture.
Ichabod's never-ending hunger shows us just how greedy he really is. And it also makes us think that even if he got what he was after (Baltus's wealth), he still wouldn't be satisfied.