Surrealism (with a capital "S") was an art movement founded be Andre Breton in 1924. "Artists painted unnerving, illogical scenes with photographic precision, created strange creatures from everyday objects and developed painting techniques that allowed the unconscious to express itself." (The 20th-Century art book.) Surrealism (the movement) is seen an an extension of Dadaism. Dadaism was an art movement that developed in reaction to what was seen as the insanity of World War I.
Andre Breton was inspired by these ideas and developed his own movement that he controlled until 1966.
Surrealism has become synonymous with strange and uncanny artwork created in a realistic way. This is art that realistically portrays the irrational or impossible. In other words surrealism has come to mean what the french call "fantastic art".