I had quite a few misses with AF on my D80 recently and I thought I knew enough about the camera... During the last ball event (where I've uploaded some pictures), I had the AF set to AF-C which means continuous focus. I thought that would be better to follow moving people. But a lot of my pictures turned out blurred (which I saw too late and on the computer). I got worried about it not working correctly. What I didn't know is that AF-C on the D80 is a release priority mode. This means that when I press the shutter button, the camera will instantly take a picture and not wait for the AF operation to finish. This explains my problem as it is most likely that I pressed the shutter a bit to fast sometimes :-(
In contrast the other modes AF-A and AF-S are focus priority modes which must acquire focus before taking a picture. The mode that would have suited me best is AF-A which would automatically refocus when the subject below the AF point gets out of focus. AF-S focuses just once.
But the topic of AF is even more complex, because in the menu there are 3 more options: Single, Dynamic and Auto. I've learnt about them a while ago, but will explain them briefly: Single here means that it will always focus just below the selected focus point. Dynamic means that it can choose a different point, when the subject moves out of focus (or another moves in?). Auto will try to focus on the closest subject under one of the 11 points (you can't choose them in this). Any of these modes can be combined with AF-A (refocus if necessary), AF-S (don't refocus -> probably doesn't make a lot of sense with dynamic) or AF-C (always refocus).
AF-S is also a designation for some of the Nikon lenses, but here refers to a built-in focus motor (servo) which results in faster and more silent focus operation.
I hope I finally understood AF. Dynamic mode is still something I've not tried a lot. Release and Focus priority were new to me and made me look like a beginner :-) Well okay, I am ^^