There's a couple of photographic techniques at use in this particular photo. The first is being able to press the shutter while freezing your bum off in sub-zero temperatures at about 12 at night and with snow falling all around you!
Actually that one's not really a photographic technique but it helps! :)
The first thing that's going on here is that you've got a flash firing. You can tell that there's a flash going off because you can see where it's hit the snow flakes falling in front of the camera. You can also see it reflecting off a point in the middle of the drum.
Flash pretty much freezes all movement because it fires at such a rapid shutter speed. So why is the drummer blurred? Because I've combined the flash with a slow shutter speed. Without the slow shutter speed the background would have been pitch black (because it was in the middle of the night).
Because I've used the slow shutter speed, the background light has enough time to record on the film (or digital) and you can see what's around the drummer. The only problem is that because it was such a slow shutter speed (about 1 second) everything that has moved during that period is blurred.
So it becomes a game of chance to a certain extent. I sat and waited and watched the drummer until I started to recognise a few patterns. I saw that every so often he would raise his arm in the air and strike a pose. So I waited until I was pretty sure he was going to do it and fired the camera (which was on a tripod).
It took a few goes until I got it just right but I think it worked pretty well in telling a story about busking at night in the middle of a snow storm. I don't know who was crazier, him or me? And of course I tipped him well afterwards.