Simply put, people talk to themselves to feed data back into themselves for additional storage and processing.
(This is another mostly-unfinished idea)
Delayed Auditory Feedback ∞
The electronic fluency device is specialized for aiding a stutterer. (Isn't it funny how stutterer is hard for a stutterer to say?) As with an audio delay, elevating or lowering the pitch or adding white noise have also been found to be useful.
Neural Connections ∞
Synesthesia is a linkage between two normally-unlinked sensory or cognitive pathways.
The classic example is when a person reads a number, they associate the number with a colour. So a white page with a black number "one" might show the number with a specific colour. Any number "one" seen in any context has a specific colour.
A particularly interesting example is with Daniel Tammet (facebook, youtube). He perceives numbers as shapes and is able to perform extraordinarily complex computations by mentally manipulating the shapes. 1+1? Add the shape for one to the shape for one, another shape is imagined and it so happens to be the shape normally seen for two.
Vilayanur S. Ramachandran has studied Synesthesia and has a lot of good videos on that and other topics.
(ted) [2007-03, @ted] - VS Ramachandran: 3 clues to understanding your brain
Evidence-based neuropsychology has a long history of noting specific damage to specific areas of the brain and seeing trends in changes to perception, thinking, personality, etc. It is more recently finding specific genetic trends, where a specific genetic variation results in brain pathways not otherwise seen.
Phantom limb syndrome may be related. I haven't looked into it recently enough to remember.
ted - further research
English, speaking and listening ∞
The English language has a fascinating history, and it's structure is almost unique in the world.
One of the annoyances with English is that the beginning part of a sentence must be maintained in memory for the rest of the sentence to make sense. When reading or listening, a person is forced to constantly predict the outcome of the sentence. I haven't done enough looking into this, but it does seem far less true for most other languages.
I have the notion that it's the properties of the English language itself which lends itself to a certain kind of mental discourse. This internal dialogue can be externalized by speech and brought back into the brain from another angle from listening, and can be processed in parallel by different parts of the brain. In this manner, a connection is drawn between the speaking and listening parts of the brain.
(I also understand that the Sapir-Whorf hypothesis is bullshit. I'm not talking about that.)