Hola Michael

We have in one sentence: "acabamos con la comida" where we've used acabar con [+ algo]; we use it this way to say "to finish something off".  This is often used when talking about food. But then we repeated the sentence using the verb in a different way: "nos acabamos la comida"; this is pretty much the same meaning but this time we are using what is called the "se aspectual" which is used with a verb to emphasise the "culmination" of an action, also used often with food: me terminé la pizza, nos bebimos las cervezas, etc.. Here is a Kwiziq lesson about the "se aspectual" with more detail. 

(I have, though, changed the text in the lesson and made the two sentences the same, so there is no confusion) 

I hope this clarifies it.

Saludos

Inma