What does it mean when a guy says to a woman you have a good day after she apologizes and he accepts?

It's really impossible to get the whole context with so little information. It seems he didn't want to continue talking about the issue and just needed more space; he may still have been smarting from whatever the offense was. This doesn't mean he didn't accept the apology. On the other hand, it may be his way of saying "ok, fine, but I'd rather not continue with this". Give it some time and don't be pushing on him; see where it goes.