Ever hear this in conversation? Ever agreed with it and had no idea what it meant? Here's a simple explanation:
Occam's razor asserts, all things being equal, that the simplest explanation is the best.
Seems to easy, doesn't it? Think about it. It's pretty intuitive. Draw 2 points on a piece of paper. What's the simplest thing to draw to connect the points? A straight line. Could you draw a squigly, curvy line between the 2 points? Sure. The point is that it "proves" Occam's Razor. Understand that Occam's Razor is very convenient (read necessary) for mathematical, scientific, or philosophical models because many high-order models involve unlimited complexity. If you use Occam's Razor, you are "allowed" to get rid of most of the complexity. Understand, too, that Occam's Razor is very necessary for very abstract arguments where there is no way to provide concrete proof (i.e., tests or observations).