Simple enough for even me to understand!
This article will help the New Ham to be more at home on repeaters and understand the operation and procedures on Ham Radio Repeaters.
It contains a basic description of a ham radio repeater, how to use it properly and is written with the NEW HAM in mind for the most popular ham band....2 meters.

What is a Repeater and Why is it Needed, and How Does It Work?
What: It's a two-way radio system that receives on one frequency, then re-transmits what it hears on another frequency; at exactly the same time. It's nothing more than a "dumb machine" with some smart people behind it.

Why it's needed: Your mobile or handleld transceiver, has a limited range due to it's antenna height with respect to the radio horizon and rf attenuating surroundings. Repeater systems are used to "transfer" your transmitted and received signals to much higher elevations electronically using large, very efficient antennas, low loss feedlines and a transmitter and receiver that is rated for heavy or continuous duty. A repeater "gets out" your signal and receives the station you are talking to with a far greater range and coverage area! You take advantage of the repeater's higher elevation to increase your effective transmitting and receiving coverage versus your mobile or hand held transceiver!