The Cybermen originally were Mondassians, Mondas being a twin planet of Earth. The Mondassians evolved more quickly than humans, specialising in cybernetics. Using their skills the Mondassians tried to extend their lifespan by replacing body parts with cybernetic components. Soon they had replaced almost every organ with machine, turning themselves into cold, ruthless, unemotional machines. Similar to the Daleks the Cybermen were left with a strong desire to survive.
Mondas left the Sol system for unknown reasons, but it wasn't long before humans started to explore space and, inevitably, meet up with the Cybermen. Alliances began springing up in the fight against the Cybermen, and there have been many wars against the Cybermen.
Also like the Daleks the Cybermen have had several redesigns. However unlike the Daleks the Cybermen, being almost entirely machine, are able co-exist with earlier, and future, versions.
The Cybermen, however, do have one major weakness: Gold is lethal. Gold coats their respiratory systems and effectively suffocates them. They are also not as well armoured as other creatures, although they do have great strength.
The Cybermen sometimes use another cyber creature known as a Cybermat. Earlier versions were much smaller, but just as deadly. The Cybermat is capable of jumping, and can be loaded with any kind of poison which it injects into the victims' necks.
The Doctor first met the Cybermen when they attempted to use Mondas to drain energy from Earth and turn the humans into Cybermen. The Second Doctor met the Cybermen on their new home plant of Telos and on the moon. The Fourth Doctor met the Cybermen when they tried to destroy Voga - the planet of Gold. Some Cybermen were captured by the Time Scoop and used as a trap for various Doctors in the Death Zone. The Sixth Doctor met the Cybermen when they tried to weaken Earth prior to the Mondas attack.
In a parallel dimension Cyberman development took a different course. They were developed on a parallel Earth as a way for John Lumic to keep his brain alive after the body had died. He then applied this to all humans. Instead of being silver the alternative Cybermen were steel. When the Daleks broke through the void between dimensions the Cybermen seized their opportunity to invade Earth.