People spend a third of their lives asleep. Most of this time is spent in some form of dream, regardless of how much or little of their dreams most people remember. So, obviously, this mysterious third of their lives can be quite important to some. Others just blow it off as meaningless, just mental pictures that the brain creates to occupy itself while you're not awake.
But dreams are far more important than that.
Once you fall asleep, after a period of relaxation and regeneration of both mind and body, your body drops into REM (Rapid Eye Movement) sleep. During this period, your mind uses dreams as a creative "vacation", or to solve problems and at times work out issues you've been having in real life. (Ever hear the phrase "Just sleep on it [a problem]"?) Your mind can use the time while you're dreaming to mull over information that you've aquired and you may wake with a greater understanding of something than when you went to sleep. Or it can replay images from your past, or create bizzare, seemingly meaningless dreamscapes.
It has been proven that deprivation of REM sleep results in anxiety, chronic tiredness, and impaired concentration. Deprivation of sleep entirely may result in hallucinations, slurred speech and perhaps insanity or even death, taken to the extreme. Face it: Your brain *needs* sleep, and dreams, to function correctly.
Some, including myself, believe that your dreams may (or may not, depending on the dream and dreamer) hold messages from your subconscious, telling you of something that you need to do, or perhaps something that is to come. Or maybe providing insight on your current station in life. The only to find this out is to analyze your dream's imagery to see what knowledge it could hold.
"Merrily, merrily, merrily, merrily, life is but a dream..."
"All that we see or seem, is but a dream within a dream."
However, I don't believe that canned dream interpretation works for people who aren't "normal". To my recollection, I've never had any dreams dealing with people, places, or events I know in real life. Cats in my dreams are kindred spirits, not enemies and not a sign of hatred. I've had dreams where I kill things, but not in a negative sense, more in a "I'm hunting down my prey" sense. Those aren't representations of repressed anger. 9/10 of dream interpretation is based upon psychology, and true, they do work for those who have normal lives, normal psyches, etc.
So what's the solution?
Interpret your dreams yourself. What does this dream-creation mean to you? How does it make you feel? While cats may be a kindred spirit to me, they might scare the $h!t out of you, and that dream may be a nightmare. Check out alternate sources of symbol meanings if you're up for it. One that I particularly like is this one. It's a page on shamanism and working with animal spirits, what the different spirits stand for and mean. It worked well when I kept having dreams about Raven, and is generally closer to my personal views on what animals represent than traditional dream dictionaries are. But hey, use whatever you feel is honest and true to the feeling of the dream. Maybe traditional symbols capture one part, but not another. Don't be afraid to "mix and match".
Oh, and another thing about sleep. Ever wake up suddenly from a nightmare or interruption and been unable to move? Sleep paralysis is perfectly normal. As part of the relaxation and reparation process in the first bit of sleep, your body releases a chemical which seperates neural impulses with the muscles they control. Just like that, you're disconnected from your body. Why does it do this? Well, if your impulses caused muscle movement even while asleep, you'd act out your dreams, wandering around or jumping and trying to fly. As you might imagine, this could be dangerous and potentially fatal. (Falling down stairs or out windows, or running into walls...) Sleepwalkers suffer from an imbalance which inhibits the release of this paralysis-chemical. And if you do some relaxation exercises before bed and keep your awareness intact, one of the fun things is that you can Feel your body going numb as the paralysis sets in.
About my dreams. Mine are odd, most often consisting of movielike imagery, lessons that I need to learn, odd, disjointed imagery, weird randomy things (Such as one dream I had which was 2-dimensional), shapeshifting, hunting things, flying, or some combination of those. Or not. I'm not me in the vast majority of my dreams, "I" am sometimes a guy, a small boy, an animal of some sort, a vampire, a bird, an animal-morph or shapeshifter, (The list goes on...), or a mere 3rd person camera angle, watching the goings-on. If you're interested in my dreams themselves, I will eventually have a record of my dreams online.
Nightmares are an aspect of dreams that I don't seem to experience, as well. I've never woken up in the middle of the night, scared $h!tless, with my heart pounding in my chest, because something was chasing me in the dark. Oh, I've had plenty of mildly disturbing dreams, such as the one where I visited hell, or a warzone (I don't know which). But I wasn't *scared*, just disgusted.