Without explanation, The Man in The Cube finds himself in a white, cubical room possessing no memory of identity or semblance of reality. During his time in the cube, 'The Man' interacts with several individuals, one of whom, Margaret, claims to be his wife, and calls him Ted. It's not clear if Ted is his name, but he does later see an image of himself with Margaret, the model of an individual who fits in with his surroundings -- a state of self which 'The Man' very much does not have.
Some of his visitors frequent 'The Man'’s cube more often than others; Arnie calls him "pal", and the proprietor of the establishment levels with him just enough to keep him mentally working through his situation. Most of 'The Man'’s visitor serve only to make him question what the state of his own reality is.
Eventually, 'The Man' discovers that his own thoughts have a direct reflection on the actions of those around him. He rather specifically describes a potential scenario that may occur if he accepts the Manager's invitation to walk through an open door: "two gorillas grab me, dressed in ballet costumes, drag me back and throw me on the floor and dance around me singing 'Home Sweet Home'." Later, he determines that a seemingly feminine character is in fact a man, "a mailman, undoubtedly", which of course, he is.
Following an attempt to take his own life, 'The Man' decides he's figured out what reality is, and triumphantly leaves the cube. He's led into an office by a man in a suit, but quickly learns he hasn't left the cube after all.