The cybermen are androids who are the second best known nemeses of Doctor Who, after the daleks.

They originated on the planet of Mondas, which was at one time the tenth planet in our solar system. It was described as being a twin planet of Earth. At this point they were not androids. Instead they were humans, or at least very similar to humans. For some reason Mondas gradually moved further away from the sun, and eventually became free of the solar system millenia ago. Because of this relocation, the planet became colder and colder, and the inhabitants had to resort to desparate measures in order to survive. They perfected the art of cybernetics, and began replacing parts of their bodies with robotics. At first they only did this with their limbs, but eventually they moved to their organs, nervous system, and eventually even their brains. In the end they had completely eliminated any of their original biological components. Unfortunately this included such things as emotions. Survival became their only goal, and relentless logic their only way of thinking.

They've threatened the human race several times. They wish to capture humans and convert them into cybermen, and they want to exploit the Earth for its natural resources. Fortunately the Doctor has thwarted them at every turn. In their first encounter with the Doctor (in the episode The Tenth Planet), not only did they not succeed in conquering the Earth, but they managed to get Mondas blown up in the process. They relocated to a planet called Telos after they lost their home world. The natives of Telos, the Cryons, were not happy about this. For some reason the cybermen constructed a tomb for themselves there, but it wasn't a normal sort of tomb, because people were able to awaken them and bring them back into action.

Cybermen are humanoid, but would not be mistaken for a human being. They are silver or grey, and have definite robotic features. Over the years, their appearance changed. In their early episodes, they looked a bit like humans wearing silver cloth, with a few other robotic features added. Later on they looked more like "real" androids.

The cybermen are extremely strong, but they do not move very quickly. Watching them cross any sort of distance is quite painful. Their primary weakness is gold. Particularly gold dust. When it is put in their chest plates, it is fatal. A weapon called the glitter gun was sometimes used to launch the gold dust into their chest plates.

The cybermen are usually led by a cyberman called the Cybercontroller. Usually the Cybercontroller is larger than the other cybermen, and may have slightly different coloring to indicate rank.

The cybermats were small, mechanical creatures used by the cybermen. They were grey or silver, and looked a little like rodents or like crustaceans. They were about the size of a rat. They have been known to inject poison, fire lasers, and make use of some sort of telepathy, depending on the episode.

The cybermen had cameo appearances in a number of episodes, but they made major appearances in the following:

The cybermats appeared in the following episodes:

Sources:
http://www.cybercontrol.org/
http://www.bbc.co.uk/cult/doctorwho/alien/cybermen.shtml
http://www.allscifi.com/
http://www.kasterborus.com/tardis/baddies/
My misspent youth