Mobile phones work because there are lots and lots of big microwave towers all over the place. When you make a call on a mobile phone it sends a signal (usually using microwaves) that goes out in every direction. This signal is 'caught' by one of the big towers. Then it's sent from one tower to another to another until it reaches a point where it can be sent out through a land line to the building you're trying to reach.
(republished on 07/17/06)