In theory, those numbers say something about the width of the tire. However, a 700x25C Specialized tire may be wider or narrower than a Vittoria 700x25C.

Tire size is one of those things you have to figure out on your own. For general riding around, I like 700x28 or 700x32. Once in a while I get a wild hair and go up to 700x35 or 700x37. Not fast in any sense of the word, but very comfortable and I never got flats with the 700x37's.