DSLR = digital single lens reflex

Basically, the advantages are that the images will have less noise at higher ISO's (important if you shoot that way, but software can help too), faster response time and more available accessories. The disadvantages are more stuff to buy and carry, and dust on the sensor is a problem that will have to be dealt with (see the post in Help about this).

I use both, and they're different tools for different jobs. Actually, I've been shooting a lot with my Coolpix lately - from studio product stuff, to nature stuff on a kayak trip, to people shots at events. It's nice to not have to carry a lot of gear but still have something to shoot with. Without it, sometimes I probably wouldn't have a camera with rather than having to carry all that stuff.