Generally, people eating together is a sign of unity. In these instances, though, Scorsese uses the idea of a family dinner to emphasize strife and discord: in The Gangs Of New York, the breakfast table with its sumptuous food, blue china, and vases of flowers directly contrasts the growing rioting and the poverty in the outside streets; it is the first thing to be destroyed. In The Age Of Innocence, the dinner table is laden with amazing food and flowers, but the company around it, friendly though they may seem, are all backbiting and treacherous society people. Likewise, in Goodfellas the dinner scenes begin by emphasizing the familial nature of the mob, where they all share food together and even the Made Men cook for everyone, but it gains a darker tone as we realize that the family attitude is only a veneer, and that the two men eating next to each other can turn on the other in a moments' notice.
Scorsese uses food as a dramatic technique in the same way that another director might use lighting or sound. It can trick the viewer into feeling sympathy for the characters, or alert them to the dissonance in a scene.
Also, I think he really likes food.