Good question. In this context, I would say that "dinner" is being used as a non countable noun. Compare: he invited me over for football. To eat dinner, to watch football.

I think Phil is generally right, but watch out for those curve-balls. 

Ex:

Correct:

"Let's have dinner tonight."

"Let's have a nice dinner tonight."

Wrong:

"Let's have nice dinner tonight."

Since we added the adjective 'nice' to qualify what kind of 'dinner' we're talking about, it's no longer a "general" dinner?

There's no simple little trick here - even advanced learners have problems with articles, so just accept that we use them and get learning. :) You really can't ignore them.

Of course, we use them to mark the nouns in a sentence.

If this helps, a means there are many of these, and we have one of them. The means that you and I know which one you mean (eg. there's only one; you've mentioned it earlier; it's obviously this one, and no others). Beware of that "concrete" rule you are taught in Russia... I find it really misleading.

We don't use articles for given names, or uncountable nouns when speaking generally. There are other phrases (eg. for dinner) that don't need an article. You simply need to learn them. :)