ALSA is, in effect, an advanced sound architechture for Linux (and other Unices). It adds features to your sound card that you wouldn't get with the OSS-free modules that are built in to the kernel, such as output to an external MIDI sound module, MIDI input, more options when recording sound, full duplex operation, etc.
There's also a commercial version of OSS, which also adds far more sound options than you get with the OSS that's included in the kernel, such as MIDI input, full duplex operation (for playing and recording at the same time), pretty much as many advanced functions as are in ALSA. OSS commercial also comes with what's called the Virtual Mixer, which allows for more than one application to play sound at the same time (i.e. playing MP3's and still being able to hear sounds from GAIM, for example). I think ALSA has something like this, too, but I don't know for sure, since I use commercial OSS instead.
I've found Arts, the sound server for KDE, to be completely useless. I use KDE all the time, and I've never come across a application, which uses sound, that required it to be on. In fact, I've had more problems with it on than I have with it off. Plus, I've noticed that the sound lags behind the video if I run the sound through the arts sound server. If I just turned aRts off and just use the OSS driver, it works just fine.
Anyway, that's the way I understand it, since I'm a bit of an audiophile, being a musician and all.
For more information:
OSS:
http://www.opensound.comALSA:
http://www.alsa-project.org