Paying a mechanic to replace the timing belt on your vehicle, which is a necessary maintenance need, can be expensive: $500 to $1,500 depending on the vehicle. The cost of doing it yourself is also expensive: 6 or more hours of time plus $100 or more in parts.
When the timing belt requires replacement, which is either at manufacturer specified intervals (typically 60,000 - 90,000 miles) or when the belt or components around it begin to fail, it's a critical need. Your engine will not run without proper timing - at best you'll lose a lot of efficiency; at worst you'll have catastrophic (and expensive) failure.
What the Timing Belt Does
For those unfamiliar with the timing belt, it's a component of the engine that creates the timing for its revolutions and fuel ignition. In a nutshell, it's what almost literally ties all of the engine's core components together so they work in concert.
It's located at the front of the engine (on one side if you have a front wheel drive car) and is usually encased in shielding to keep grease, oil, debris, etc. off of it.
The timing belt runs from the engine's crankshaft (typically at bottom center) up to its camshaft(s) (typically at top-center if one, or top on either side of two). In between there, it will also run through and rotate the water pump (which moves coolant around the engine block) and sometimes the distributor (though this is rare).
As the crankshaft spins, it rotates the belt around this circuit to turn the camshafts, etc. The rate at which the crank turns determines the spinning rate of the camshaft which in turn opens and closes valves and (either manually or electronically) determines which cylinder is getting fuel and which are exhausting. If the timing is not perfectly aligned, then the wrong cylinder will receive fuel or fuel and air for ignition will be inserted at the wrong time or volume, causing the engine to run roughly or not at all.
Without the timing belt, the entire engine will do nothing. All systems depend on the timing being correct.
Most mechanics replace several core components when replacing the timing belt, such as the water pump, idler pulley, and timing belt tensioner since all of these things require the same removal of objects that the timing belt requires, so replacing them is preventive maintenance.