To be precise, it was the first time a computer beat a the world champion under classical time controls.  I've found several good sources of analysis of the Kasparov - Deep Blue games, but I must admit I'm rather partial to Wikipedia in general, so here's a taste:

http://en.wikipedia.org/wiki/Deep_Blue_-_Kasparov,_1996,_Game_1

In particular, it explains clearly why Kasparov resigned: in as many words, he no longer had any question that Deep Blue would eventually be able to mate him.  ;)

Cool thanks guys. It was surely resignation. BTW it was Kasparov vs. Deep Blue 1996. This was the first time a computer beat a grandmaster.

check mate wins usually happen if both players are beginners.....in grand master and international master or high level player it is unusual to see check mate because they know what happen next....and they know it is better to resign than to proceed to check mate....

Truly the soul of wit, nmplayer.  And what exactly does your Helping Brothers w/Chess group do, then?

The rules of chess say that either player can "resign" the game at any time, meaning that they concede defeat: the other player instantly wins.  This is typically done when the losing player feels that their opponent has conclusively demonstrated that they will eventually win if the game continues because of some overwhelming advantage.  This is an extremely common practice among higher caliber players: checkmate is almost never executed over the board because both players can sense the inevitability of the outcome well in advance, and neither would have any difficulty actually playing the winning side from the point at which the loser resigned through to the mate itself.

The other possibility is that one player lost the game by running out of time, which happens occasionally.  This occurs most often right before the "time control" moves - the moves at which the players receive more time to play the remainder of the game - which are usually moves 40 and 60.

Resignation...?