Throughout the day you collect lots of miscellaneous facts. Almost none of this gets put into long term memory until you sleep. If your sleep too short, some of it gets left out of long term memory never to be heard from again.

Think of it like this: you have just thrown everything in your apartment on the floor, thus nothing is organized. Eventually it would be hard to find things. In trying to find specific items, you break your belongings, unless of course, you are extremely careful. So, you call a maid in to clean up while you step out.  The maid is smart and knows exactly where to put everything so you can find it later.

When you sleep, it is like that smart maid comes into your brain.  Your brain goes into hyper drive to clean up all the facts from the day and put them away for long term retrieval.  Some facts that were not very important and you thought about only once get discarded so as not to clutter up your long term memory.

If you only sleep a short time, it is like interrupting the maid.  Not everything is cleaned up and put away.  Some people have more efficient maids and only need 6 hours of sleep, but most people need more to get all the information from the day cleaned up and organized.

People who go days without sleep really begin to see drastic effects.  If they go long enough without sleep they can even begin to hallucinate.  The human brain has evolved to only hold so much information before it needs to get organized.  Its like reaching a point when you your is so full of stuff you can longer walk around in it, much less find anything.

If you fall asleep with a problem on your mind, your brain will even work on that while you sleep.  Sleep is an especially good time for the brain to work on problems that you are stuck on trying to figure out.  Your brain can be very creative during this time and often you can awake with a brand new solution to try.  So, do not stay awake trying to figure it out, but sleep on it.

So for your brains sake, get a full nights sleep so that all the prior days information is properly put away and you can begin a new day with lots of room for new information.