A renewable resource is any resource that can "renew" itself within a person's life span. But most renewable resources become exhaustible if we use them faster than they are renewed or replaced by nature.
Examples:
Ground water is a renewable resource. In recent years, there is a decline in its level because its usage is faster than its replacement. This has led to the drying of wells.
Forests or trees are being cut down to fulfil our need of wood for furniture, paper etc. It usually takes 25 years or more for a tree to grow to its original state. If new trees do not grow up and replace the older trees as fast as the older trees are cut down, sooner or later they would be exhausted.