What is cleared when I restart my phone? I haven't restart my phone since the day I got it however decided I would give it a go since my contacts seem to disappear intermittently. Anyhoo, it prompted me that if I restarted my phone anything stored in memory would be cleared. How do I find out what is stored in memory and what is being cleared?
Things that would be cleared are anything that isn't saved, open applications, etc.  For example, if you were playing a game, and just pressed the home key the game would go to the background and be paused.  When you restart your phone, you will lose that game (up until the last point it saved).

Other things that you leave half finished, such as an unwritten email might get lost, but even that is unlikely because I notice Android pretty much makes sure I never lose anything.

It's not a bad idea to restart your device once in a while, but you really do not have to worry about losing anything.  It's safe.