It's a shorten form of "pongamonos a comer".
The verb is "poner" in its imperative form:
ponte a + infinitive
pongamonos a + infinitive
ponganse a + infinitive
¡Ponte a trabajar!
¡Pongamonos a trabajar!
RAE defines this use:
41 . prnl. Comenzar a ejecutar una determinada acción. Ponerse A escribir, A estudiar.
So basically it means "to begin doing something".
In the shorten form depending on the context you can infer the pronoun. In your example because it was a family and most family eat together the pronoun was "nosotros" thus "pongamonos a comer".
In its imperative form it is used to command. I don't know if it is used in all Spanish speaking countries but at least in Mexico is used.