A Death Match is a professional wrestling match in which the match doesn't end until one guy DIES!

Oh wait, no, that ain't it at all.

A Death Match is a professional wrestling match that takes place in HELL!

Er, no.

A Death Match is a professional wrestling match which does not end after just a pinfall.  Instead, after a pin, the pinned wrestler has 10 seconds to get to his feet.  If he does, the match continues as normal.  If he does not, he loses the match.  A location is sometimes prepended to the name--Texas Death Match, Florida Death Match, etc.  The rules remain much the same unless it's a Japanese Death Match, which is very, very different.

The Death Match is kinda wonky.  It can be very suspensful, since the crowd is on the edge of their seats seeing if the wrestler will be able continue, but the ten second "gaps" with nothing really going on (which the wrestlers use to rest) can also make the match seem very disjointed.  That's a big reason why you don't see many of these kinds of matches--just about the last one I can remember was Cactus Jack vs. Vader at Halloween Havoc '93 (a terrific match, incidentally).