By using the article (a) you are indicating a specific. Even when it's the indefinite article, it's still referencing a specific school.
When you say you go to school, that doesn't suggest to us which one it is, or, for that matter, does it even suggest that there is only one school you attend. By saying you go to a good school, then in your mind you are specifying a single, particular, specific school, even if you haven't told us which one it is.
By using the indefinite article (a/an), you are allowing that there may be other good schools. You just go to ONE of them. Someone else may attend another ("an other"). If you used the definite article (the), then your rather presumptuous claim would be that your school is the only good one in existence: I go to the good school.
The definite article is entirely appropriate (although it may be omitted entirely) when you say, I go to the University of Arizona as there is only one of that name. Sometimes, it is best omitted. I go to Oxford College. That's a separate debate on why sometimes in, sometimes out. Common usage, I guess, was the best answer we came up with here, when we went over that one a few months back.