A timing belt is made of rubber and may be reinforced with braided steel. A timing chain is made of metal.
On most vehicles (not all) if the timing belt (or chain) breaks while the engine is running, it can cause internal damage to the valves (and of course your engine will no longer run). It is best to replace the belt as per instructions, either by age or mileage whichever comes first.
Rubber (even synthetic rubber) breaks down with age, which is why it is recommended to be changed at 8 years.
When changing the timing belt change the cam seals also. If does not make sense to change them later especially when you're in the same vicinity