If I might indulge a current hobby horse, I've been playing with the idea that language is the simplest thing humans do that requires a computational account. From this premise it follows, for example, that however the minds/brains of chimpanzees, dogs, bees, ants, or c. elegans work, it's not through communication. Something else is going on, complex dynamics, for example. OK.
I'm thinking that all these bumps, hesitations, fillers, whatever, of conversation betray the inner workings of these mechanisms. We've got, say, a dynamical system implementing a computational process, speech. And it doesn't always go smoothly. The right word or phrase isn't always available; it's not like they're all queued up just waiting to be entered into the speech stream. So the system has to hunt around looking for them. That is, we're listening to and making sense of our own speech via the auditory system even as the motor system is placing words into the speech stream.
Now, when we write, he can clean things up so it appears perfect. The language computer can parse those sentences readily (that is, map words and phrases onto semantic structures) and it all makes sense. But we all know that writing can often be quite difficult. We have to do quite a bit of reworking to produce computationally fluid prose.