It's supposed to be a representation of one's thought processes. Of course, true stream of consiousness would then always be about stream of consiousness itself because when the author sits down (or stands, or kneels, or lays down as the case may be) to write a consciousness stream, what is going through his mind is something like "Ok, stream of consciousness, gotta think of something.... ok, what am I thinking?" Thinking about thinking can be rather confusing. Thinking about thinking about thinking, can be even more so. Therefore I take a step back and say "(Thinking about^X + thinking; X=1 to infinity)" But now having defined that I have created yet another level- hoisted by my own petard, you might say. So that leaves us with naught but to ignore the meta-level thought processes and create stream of pseudo-consiousness, which nevertheless must be inherently interesting, because I like long-strung-together-by-hyphens-words.
Don't you?

A literary technique pioneered by James Joyce that narrates the thoughts of a character in a literary work. The most notable works employing stream of consciousness are Ulysses by James Joyce, both The Sound and the Fury and As I Lay Dying by William Faulkner.

Here is an example, taken from James Joyce's Ulysses:

The priest's grey nimbus in a niche where he dressed discreetly.
I will not sleep here tonight. Home also I cannot go.
A voice, sweetened and sustained, called to him from the sea.
Turning the curve he waved his hand. It called again. A sleek brown head, a
seal's, far out on the water, round.
Usurper.

Stream of consciousness is more common today than it once was, however it is employed more conservatively.