With the addition of Recent Activity a while back it became much easier to know what's going on. However, sometimes when a badge is awarded, it's not immediately clear why it happened.
I suggest that some awarded badges (those that can be be awarded several times) a little bit more verbose, for example, in the Recent Activity page it should say:
[Jun 27] awarded [● Nice Answer] for link-to-question/answer.
Jeff mentions below that the discovery is part of the fun. He mentions a parallel to the Xbox achievement system, but from what I can tell, an achievement for 'A Perfect Lap' is not ambiguous, nor is "Launch a Gnome into Space" in Half Life Episode 2.
But "Nice Answer", which can be awarded several times, is not the same - it's not precise enough. I have to go to the Profile page, sort answers by votes and then try to remember which answers were previously awarded, and which weren't. Sometimes it just becomes too much of a hassle to hunt for this information.