It means like an artificial plot thing in a story that comes out of nowhere and saves the day. (No offence Deus )

Anyway, the subconscious is primitive, and when you give it a problem to work on, it keeps on working on it until it figures out some answer to its satisfaction. That's why, when you can't think of somebody's name or something, later on it will just pop into your head, because you gave the subconscious a problem and it worked on it until it figured it out. And that's also why you should never ask yourself negative things, like "Why did I do such a stupid thing?" because your subconscious will keep trying to find the answer and may come up with something bad, like "Because you're an idiot.", and then you tell yourself that. You should always ask positive things that you want to know the answer to, like "How can I do (blank) better?" and the subconscious will work on it and give you the answer. (I ask myself how to LD better all the time tho and my stupid subconscious doesn't help me at all.)

So I think you have become aware of this process "Caught your brain thinking on its own" as you say. That is actually pretty cool, I think. I guess I have sort of done that as I was drifting off to sleep and get woken up, I mean suddenly realize I am thinking about something I wasn't consciously aware of.