What does Occam's razor mean?
A summary of Occam's razor
Occam's razor, in theory, means that when there are multiple hypotheses or theories that can falsifiably explain the empirical data without contradiction, the simplest one should be used. It is, however, important to take a science-based approach to what simplicity means. Otherwise, simplicity can mean many things, some of which are incompatible. For example, to measure simplicity in how easy it is for some people to read the text would be a fallacy of confusing content with formulation, and the figures would also vary depending on who the readers were.
The scientific approach
A science-based approach is to eliminate extra steps that make no additional falsifiable predictions. This includes but is not restricted to claims that only move a problem. For example, claiming that a deity created the Universe does not solve the question of where a deity is supposed to have come from, so simply say that the Universe came from nothing instead saves one step. Occam's razor prefers the atheistic Big Bang theory over cosmological creationism.
How to measure complexity
However, when a more "complex" hypothesis or theory makes falsifiable predictions that the simpler hypothesis or theory does not make, things are very different. In that case, the difference in falsifiable predictions makes them incomparable, so Occam's razor cannot choose between them. See also splitting a H/T page. At least this lack of comparison applies at the local, specialized H/T scale. An unified H/T that makes all the same predictions as a multitude of other H/Ts, but from a single premise, is simpler at the grand scale and therefore preferred by Occam's razor. This is what drives unification of science towards theories with a more general applicability. Scientific Method Wiki is created to let this work efficiently, which fragmented peer review journals quibbling about what "field" or "discipline" something is in cannot do.
Complexity is secondary to empirical facts
Empirical falsification, however, always takes precedence over all Occam's razor considerations. No matter how simple a hypothesis or theory is, if it does not describe reality, it is false. See also universal fallibility.