What is Ockham's Razor?

Ockham's razor (or Occam's razor, Achem's razor) is the argument that in order to understand something, we shouldn't invent elaborate explanations that use useless information. The Galilean library gives the crop circles phenomenon as an example, explaining that a popular belief is that
 crop circles are caused by aliens, usually with their aircraft, while others believe that they are the work of guerilla artists or those making the circles an elaborate hoax. Ockham's razor would argue that since it can't be proved that aliens cause the crop circles, they shouldn't be used as a part of the explanation for them. As the Galilean library states, "we should pick the simpler explanation", especially since people have been able to reconstruct the crop circles. (1)

A page on University of California, Riverside's website by Jose Wudka explains that while Ockham's razor can be simplified as "keep it simple", it is a more complex and effective argument. The page states that if there are two possible explanations for something, experimenting should prove which explanation is better, and if they both reach the same conclusion, opt for the one that doesn't have "additional baggage". (2) If you left a plate of cookies on the living room table, then return to find most of them gone, you could obviously conclude that someone ate them, but if you conclude that it was either the work of your roommate or leprechauns, you're better off asking your roommate if he helped himself to the treats. Unless you see leprechauns wandering around your home, there's no reason to think the Irish creatures helped themselves to the cookies.