A radio repeater is basically a radio receiver, and a radio transmitter in one unit.
The receiver part receives a radio signal from a walkie talkie or mobile two way radio on one frequency, and then re-broadcasts it out again on another frequency.
The point of a Radio Repeater system is to increase the broadcast range. For example a handheld walkie talkie may only have a range of a few miles, and is fairly line of sight.
With a repeater the fairly weak signal from a handheld walkie talkie (5 watts on VHF for professional equipment) is re-transmitted at maybe 25 watts of RF power. Thus the signal can be heard further away.
Repeaters are also useful when there are hills in between two radios wishing to communicate, as is the case at the relatively high frequencies that private business radios operate on. As the signals are mainly line of sight, a repeater located on top of the hill can receive the signal from one radio, and re-transmit it, which can be received by the radio on the other side of the hill.