"Big Brother" is a dictator in a totalitarian state, taken to its utmost logical consequence. In the society that Orwell describes, everybody is under complete surveillance by the authorities. The people are constantly reminded of this by the phrase "Big Brother is watching you", which is the core "truth" of the propaganda system in this state.
The physical description of "Big Brother" is reminiscent of Joseph Stalin. In the novel, it is not clear if he actually exists as a person, or is an image crafted by the state.
See also: Big Brother television program, Survivor