The timing belt controls the valves on your engine and wears out over time. Depending on your engine design, if your timing belt breaks, the pistons can crash into the valves and your engine is more or less ruined. In short, by not replacing your timing belt according to the interval specified in your owners manual, you are running the risk of ruining your engine.
The timing belt itself is relatively inexpensive, however, it usually requires quite a bit of work to get to and that is why the procedure can be costly (depending on your engine design.) Some cars will have the water pump or other components connected to the timing belt - if your mechanic recommends changing the water pump when he is replacing the timing belt, take him up on his offer. The cost of the part is negligible compared to the amount of work needed to access it.
Some engines employ a timing chain instead of a belt - timing chains typically last the life of an engine and don't need to be replaced on a regular basis.