Serial dreams are, to me, one of those weird phenomenons your subconscious
likes to play on you. Basically, it's when you have a dream one night, and then what is essentially a continuation of that dream another night. Might like reading a serial comic
There are many scientists who study the mechanics of sleep and dreaming...study about the phases of sleep and REM sleep and whatnot. I don't know too much about it, but my personal theory is that your subconscious has issues that it rehashes often, during your sleep. A less likely (or so I'd like to think) theory is that most serial dreams are illusions of the consciousness, when you have a dream so clear that you're sure you've had it before...
For me, serial dreams are usually all related to some event. It might be a real event. It might have happened in the past. Perhaps it was unsatisfactory and your subconscious has decided to rewrite a more favorable outcome. It also might be event that will happen in the near future (always in the near future, like a few months or less) and you see the optimal scenario according to your subconcious. I find that usually, when the serial dreams are about a real event, it is your subconscious projecting a favorable scenario aboutpast or future events.
On the other hand, it might be about a totally irrational, fictional event. I once had a series of dreams where I got arrested, you know, by the police. I forget exactly what I was arrested for, or how the serialization of the dreams worked. (it's not like Star Wars though, serial dreams usually overlap quite a bit rather than one picking up where the last left off. Serial dreams aren't recurring dreams, though, because there is usually some progression of them.) Needless to say, though, I've never been arrested, and I still can't figure out why I had a dream about that.
So basically, serial dreams can be just as clear or just as nonsensical as normal dreams, they just sort of are an extended form of dream that happens over time. Also, my personal experience is that I never recall having them until around the time I turned 15. I don't know if they happen to everyone, but they do happen to me. I think it might be a side effect of your thoughts becoming more complex, and your subconcious thinking it might need more time to "dream things out", rather than just one session of REM.