Nonrandom survival of random variations. That's about as simple as I can make it.
Most of the other explanations given in this thread should be useful, with the obvious exceptions of Legolas who is for some reason recommending superstitious nonsense that has nothing to do with the subject, and of course Warlock who is unjustifiably proud of not understanding the first thing about evolution.
To really understand evolution may take a bit of work. If it was that easy, someone would have figured it out before Darwin! However, there are shortcuts: http://talk.origins.org is an excellent resource which will probably be able to answer any specific questions you have. If you want a simple introduction, Richard Dawkins' DVD "Growing Up in The Universe" is available from http://www.burningshed.com/rdshop.asp