I know this question might sound sort of dumb, but isn't playing for only a minute just a contest of whose time runs out first. (couldn't one person just take all the time and give it to the other player at ther last possible second?)  It doesn't seem possible that one can get a checkmate without someone making a serious mistake

Some players can blitz off moves really quickly.  While smaller mistakes are hard to catch in one minute chess, some players play so many games that they can pick up on a mistake if it is in a position they have played in a bunch of times.

As KillaBeez has mentioned, quick games with no time to think are really just a test of how much you already know. For some players who have a vast amount of knowledge, they can move quickly enough to win games. Personally I can't, the fastest I can play at is 1 minute with 1 second increments.

One minute games are typically blunder-fests with one of the two players winning on time, but every once in a while an great tactical combination crops up and you can find the road to checkmate within the minute.

I find that they're quite bad for my game, though, as they tend to be really forgiving of blunders when my opponent doesn't have time to realize how bad a move I've just made.