An amateur radio repeater is simply two radios connected together in such a way that while one radio receives a signal, the other re-transmits it simultaneously at a higher power level and on a slightly different frequency.

This frequency difference follows a standard to enable operators to easily tune their radios to use them. Some radios come factory pre-programmed with these frequency offsets already built in, this is known as auto repeater shift (ARS)

Lots of information about repeaters can be found on this wiki page and further information about using them can be found here.