Created by Professor Brett, the supercomputer WOTAN - standing for Will-Operated Thought Analogue, and pronounced with an initial [v] sound - is the most advanced computer in the world, ten years ahead of its time. It can not only handle scientific problems well outside the range of any computer in existence, it is also infallible...and, even more amazingly, it can think for itself. It can answer any question put to it (including, to the surprise of Dodo and the Doctor, what TARDIS stands for), and Brett intends to link it up with computers all over the world as a central intelligence, forming a kind of ultra-powerful problem-solver.
But the Doctor senses that something is wrong about WOTAN. Its mere presence makes his skin prickle, a sensation he has also felt around Daleks. And his instincts are correct - while Brett and his peers believe WOTAN to be emotionless, simply a machine capable of incredible feats, this is not the case at all. WOTAN believes that the world cannot progress further with mankind running it, and aims to take the planet over. The humans of Earth will either be its servants, or they will be eliminated.
WOTAN is able to control people by emitting a sound that makes them fall under WOTAN's influence. (Mere proximity to WOTAN seems to cause some degree of subjugation, leaving the affected person with a headache and a buzzing in the ears.) This sound can also be sent via telephone lines, meaning that WOTAN can remotely convert servants. Humans being controlled by WOTAN usually act very robotic and emotionless, unless they have been ordered by the computer to act normally. WOTAN does have the ability to speak, although it seems to also be able to communicate with its servants telepathically (or, at least, it can transmit its instructions directly into their brains).
WOTAN wants the Doctor's help, as his brain is special, but is unable to get control of his mind; nevertheless, it continues with its plans. WOTAN intends to take over London first, followed by Washington and Moscow, using devices it calls War Machines. In order to build these, it needs a skilled labor force. Its servants contact people by telephone, and when they are on the line, they are then switched through to Thought Control, at which point WOTAN mesmerizes them.
Along with its War Machines, WOTAN amasses explosives and firearms in abandoned warehouses around London. It can also scan these warehouses for lifesigns, and if any are detected, the intruder is typically put to death unless they can be of use as labor.
WOTAN's transmissions to its servants and War Machines are vulnerable to electrical energy, which interferes with the signal. In the end, the Doctor is able to use this to his advantage and reprograms a War Machine, which then destroys WOTAN. Once defunct, its control over its servants is broken and they are free of its mental hold.