"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. The Party line would appear to be that he is a real person, who was one of the founders of the Party along with Emmanuel Goldstein, and is universally so well loved he is called by his nickname. His real name is unknown to Winston Smith.
Since the publication of 1984, the phrase "Big Brother" has entered general usage, to describe any overly-inquisitive authority figure or attempts by government to increase surveillance.