Ockham's razor doesn't just say "pick the simplest explanation", but more specifically applies to
concepts (
entities). It states that concepts should not be assumed when explanations do not need them.
The canonical example is the theory of ether. In the 19th century, physicists explained the transmission of light, and electromagnetic waves in general, by assuming the existence of an invisible substance filling the universe; this substance was called the 'ether'.
Modern physics does not need this concept: the razor has eliminated it.
This nicely illustrates the opening remark: the reason we speak of Occam's razor here is that a concept was eliminated, not that theory was simplified; the hypothesis of ether was in fact replaced by a more complicated theory.
This razor may seem a simple tool of the mind, but it stands for an important shift in attitude in Western intellectual life, that first developed in Ockham's own time, the Renaissance, and gained force, particularly in the Anglosaxon world, up to the present day.
In scholastic thought, wisdom consisted in understanding the words of earlier wise men; it was the task of the intellectual to understand them and apply them in the real world. Words are put first.
In the newer scientific mode of thought, observed reality is put first: words, concepts, theories, are only tools to describe reality, and like all tools, they can be replaced by better ones. Wise words and concepts from the past are simply discarded when better explanations of reality are found that do not depend on them.
To a scholastic thinker, truth is found in books; what we have to do is understand them and see how they apply to our lives. The Bible writes: in the beginning was the word. Plato writes: reality is formed by the imperfect manifestations of absolute concepts. Descartes says: I can build up knowledge by pure reasoning, by carefully defining what my terms mean and exploring the logical consequences.
To a scientific thinker, the truth is out there; we cannot really capture it, since every truth is stated in terms of concepts, and concepts may turn out to be obsolete; the best we can hope for is certainty. This view is represented in the history of philosophy by Hume and other philosophers of the British school of empiricism.
If you ask me, the present-day battling between religion and science is really a manifestation of this difference in intellectual attitudes:
In religion, the word is a given. The stories, explanations, concepts and formulations provided by the Holy Scripture are unquestionable: we can annotate them and interpret them, but considering whether they could be replaced with different, more accurate words will immediately take us out of the realm of (Christian) religion.
In science, on the other hand, the word is just a working tool. Darwin makes an honest attempt to explain how evolution works based on what he observed, but his words may be replaced with better explanations, should they come along, since what really matters is not the words, but the actual world and how it works.
This explains why the creationism debate is so thoroughly unproductive; the collision is not about matters of fact or explanations of facts, it is a collision between the scholastic and scientific intellectual attitudes. From a scholastic viewpoint, Occam's razor, or for instance, the notion of a scientific theory held in science, are utterly nonsensical. God-given concepts on the other hand - starting with God - are impossible to understand from a scientist's point of view.
Thanks to Purvis for remarks.