Clincher tires are the normal kind, that fit into the rim with the tube inside them. Tubular tires are also called "sew-ups" and are glued down to the rim and the tube is inside them. I'm might be buying a bike to turn into a fixie that comes with tubular wheels, so I've been trying to decide if it'd stick with the tubular wheels (suicide hub until I build/buy a proper rear, and then a question of clincher or tubular for that), or switch to clinchers.

Anyway, http://www.sheldonbrown.com/gloss_tp-z.html#tubular is what sheldon has to say about tubulars. If you're buying a new wheelset you probably want to go with clinchers for the ease of it. If you're buying tires for a bike, you probably have clincher rims.