Most dreams can be interpreted. I interpret my dreams as well as the dreams that my friends have. I find that your dremas depict something that is either currently going on or will soon happen. Its not a premonition, its just basically saying if you have a dream about dieing, Sometimes people have that cream, its quite common. The dream is not about physically dieing. But a stage in your life that your finally getting over or a period of time where you've just accomplished something and your moving on. Its a good sign. Even though in our awakened states death is death.
Most dreams are violent or cute, or make no sense at all. This is also depending upon your day. Though when you go to sleep you dream about 6 -7 times a night with each dream lasting about 15 minutes or more. Some people don't remember their dreams and most people would say that "only the artistic people remember their dreams." I know this not to be true because I've known some very inartistic people to remember their dreams.
There are four stages into sleep. I know that I will have to do more research for you and I'll get back to you on that.
REM - Rapid Eye movement:
Main Entry: REM sleep
Function: noun
: a state of sleep that recurs cyclically several times during a normal period of sleep and that is characterized by increased neuronal activity of the forebrain and midbrain, by depressed muscle tone, and especially in humans by dreaming, rapid eye movements, and vascular congestion of the sex organs -- called also paradoxical sleep, rapid eye movement sleep
Thats a general definition of REM From Merriam-Webster.
But like always we resort to Wiki! This page is actually a really short but very informational read on REM:
http://en.wikipedia.org/wiki/Rapid_eye_movement
----
My dreams are dark, and they normally involve me killing something or something killing me. Rarely do I have a dream that makes sense, but I normally am able to interpret them pretty well.