Truly nobody knows, it's an open research question. And to complicate matters more we know (as others have mentioned here) that everyone doesn't think in the same way.
As an aside, there is a theory called the "bicameral mind" which posits that this internal dialogue is the source of religion. In ancient or rather even prehistoric times, it's theorized that people started separating themselves from the voices in their heads in a spiritual way and this gave rise to the concept of a "God".
What I find interesting is that supposedly, not everybody actually has an internal monologue, I just can't even imagine what that must be like. But then I start to wonder, do I even have an internal monologue, is what I experience an actual "internal monologue"? I assume that I have an internal monologue, I definitely talk to myself and I have thoughts running around my head all the time, but I don't know that I "hear" an internal monologue or what having an internal monologue is supposed to be like. Is what I experience the same thing as what everybody else is experiencing?
Chomsky would say that the original purpose of language is to structure thought, with communication being solely secondary. (Or something like this, I don't recall it word-by-word.)
If that's correct, then internal monologues are simply a result of your brain processing your thoughts.
I consider myself to have an internal monologue, but it doesn't just run all the time. Like, sometimes my thoughts have words, and sometimes they don't. Is it like that for the rest of you who have an IM? I always assumed it would be, but considering some people don't have one at all, it wouldn't surprise me that much if some people had one constantly.
I really tried to word this in a way that makes sense.. sorry if it doesn't lol.
I'm by no means a medical expert, so just a stab in the dark here - our brains constantly process all sorts of information. Whether that's memories, input from your various senses, or a million other things. During that process, your brain is also trying to make sense of it all ("Why?", "What does it mean", "How?", etc).
Our ability to communicate and express language is intertwined in this process, which of course is what gives you the perception of dialog. So in essence, I think its just our brains trying to make sense of... its process of making sense, if that makes sense?
On a side note, I'm practically dosing myself with semantic satiation with how many times I've used "sense" here (that last one being more tongue-in-cheek)...
My guess would be it's a side-effect, kind of like pareidolia. Us being extremely social animals, so much that being cast away from the tribe in our hunter-gatherer days would spell certain death, our brains have become extremely attuned to face/emotion recognition and language. So we have a tendency of using words to express ideas, even to ourselves.
I use it for reasoning. It's a way to talk to myself without having to do so out loud, which I do a lot.
There is a segment of the population who, apparently, don't have one. Even deaf people apparently have an inner monologue of hand signs visualized. But this segment just lacks one entirely. I don't understand how they think, how they come to a conclusion. Things just pop into my mind, when I take my mind away from other matters and let my subconscious bake on an item... is this the way they think about everything? I don't know.
I think I think differently than most. I have a very active internal monologue but when it comes to visual thought I can very easily overlay my thoughts onto my vision. Almost like a diagram or writing something on something but in my head only. I feel that if I was smarter I would be able to do something with it.