Context is the historical moment in which a piece of art is produced. It is the intersection between an artist's personal history, the history of, and movements within, a medium and geographical location.
All art has two basic meanings. The first is its aesthetic and technical meaning, without consideration of context. The second is what the art says or means about the politics or culture of the historical moment in which it was produced.
Leni Riefenstahl's 1938 film "Olympia" is a documentary about the 1936 Summer Olympics hosted in Berlin, Germany. Its technique and aesthetics are impeccable. It uses many cinematographic and editing techniques (including smash cuts, juxtapositions, and canted camera angles) that were unusual for the time but later became more widely used. However, along with Riefenstahl's 1934 documentary "Triumph of the Will," it was funded by Adolf Hitler and is considered Nazi propaganda.
"Olympia" is an extreme example of a piece of art that was significant in and out of historical context. Some art is very self-aware. An example of an artist that created his own context so thoroughly that the context became part of the movement is Andy Warhol.