Occam's Razor is a logical principle that holds that one should should not make more assumptions than is needed. In other words, the best explanations are the simplest ones. E.g. if we were modeling a few datapoints on a graph, it would make sense to find the simplest curve that encompasses them all, rather than some convoluted curve that fits the data just as well.
Occam's Razor is often invoked by the atheist argument that we can explain everything without introducing metaphysical concepts such as God; bringing God into the picture adds unnecessary complexity.
Bob's Corollary
The more powerful the entity, the less likely it is to exist.Explanations that attribute 'everything' to the existance of a God are suspect because they are untestable. E.g. If I had a scientific test for the existance of God like a litmus slip that turned red to indicate that God did not exist and the slip showed red, this result could be explained away by arguing "God changed the rules so now red means God exists".
-Bob
Strong theories make testable predictions that have proven true time after time. A theory that invokes an all-powerful God that can change the laws of universe at any moment escapes falsibility. So, in other words Bob's Corollary says that theories that rely on omnipotent beings are weakened by the fact they potentially can never be refuted.