Computers play chess by brute force. Using recursion the computer program examines each move, both its own and its opponents, and judges which would work out best. Of course doing this for just the next move would quickly lose it the game, so the computer not only examines the next move but dozens, hundreds, if not all possible future moves.
Older hardware limited how far ahead the computer could look, since each iteration takes a finite amount of processing power and time. New computers and chess playing games don't have that problem. When you tell it to play at an easier to beat level, most likely you are adjusting how many moves the program is looking ahead.
Thinking Machines has put a great demo of this recursive chess playing online. As the computer thinks through all of its and your possible future moves a very faint line is drawn on the screen. The more it examines a given move, the more lines that are drawn and the thicker the resulting line looks. Fun to watch. Also interesting is to try and decode the lines, picking moves that seem to make the computer nervous.
It's fascinating to watch. Even makes losing fun!
You can win?
I never win Chess...
No, I mean it makes *my* losing fun! I'm very rusty at it, so I always lose, too. I used to play at least once a day for years, but that was in the late Baroque era.