Take a look at the Wikipedia article under the same name and them let's try to figure it out with an example outside form literature.
Sometimes, when something is labeled one way or another, it becomes biased with a mist of complication or unintelligibility and most people (me included) simply dismiss it as too complicated or "it is not for me", and the like.
In the article above it is said, and I quote:
"Possibly the most famous use of the technique came in 1922 with the publication of James Joyce's Ulysses"
and since Ulysses is obviously an obstacle, the point is made.
Before giving our example outside literature, take a look at this famous picture and a very interesting report on it:
The report claims it was not staged, but she is reading the last page...(you didn't notice, isn't?...)
The example on Stream of Consciousness outside literature is this: Fiction of Something
If you realize that it is simply a glorified catalogue of Furniture, I cannot refrain myself to observe that Ulysses is a glorified version of the following:
"Makes breakfast for his wife. Goes to the butcher. Goes to the post office. Goes to church. Goes to a chemist. Goes to a public bath. Goes to a funeral. Goes to a newspaper press. Goes to a locksmith to canvass an ad. Feeds some seagulls. Goes to a bar. Helps a blind man cross the street. Goes to the museum. Goes to to the library. Visits a bookseller. Window-shops. Goes to a restaurant. Listens to some live music. Writes a love letter. Goes to another bar. Nearly gets in a fight. Masturbates to a beautiful eighteen-year-old exhibitionist giving him a private show. Takes an alfresco nap. Takes up a collection for a widow. Goes to a hospital to visit a pregnant woman. Flits with a nurse. Feeds a stray dog. Goes to a whorehouse. Helps avert a row with the police. Goes to a cabman’s shelter and listens to a sailor tell stories. Breaks into his own house. Urinates under the stars with another man. Watches the sunrise. Kisses his wife on her arse."
From Biblioklept