The text that would most likely be written in a stream-of-consciousness narrative style is a journal entry . Stream of consciousness is a method of narration that describes events in the flow of thoughts in the minds of the characters. A clear example of this is The Catcher in the Rye.
The term refers to the fact that nothing is joined, the thoughts are written as they pop up in the characters' minds. It flows, just like a river or a stream.