Occam’s razor is a principle of inference which is often stated as ‘the simplest explanation is most likely to be correct’. This, however, is a misstatement of the idea as it was originally advanced by the medieval philosopher William of Ockham, nor does this accurately describe its application in the sciences. More correctly, Occam’s razor states that, all else being equal, explanations with the fewest new assumptions are to be preferred. Such an explanation requiring few or no new assumptions is said to be parsimonious.
For example, if I came home to find my house ransacked and many valuable items missing, one way to explain this would be to posit that my house had been burgled. This explanation only requires the assumption that burglars entered my house, which given our background knowledge that such things are not uncommon, is a fairly plausible assumption. An alternate explanation which would equally well account for the facts would be that a poltergeist ransacked my house, moving some items and causing others to disappear. Since the existence of poltergeists is (presumably) not part of our background knowledge, we must first posit the existence of poltergeists that ransack houses, and then further post that a poltergeist actually was present in my house at the time in question, and furthermore that the poltergeist had some reason to selectively make only valuable objects disappear (perhaps because they have some perverse sense of humour). This poltergeist explanation seems outlandish, and Occam’s razor provides a clear reason as to why. The reason is that, in order to explain the ransacked house and the missing valuables, this explanation must introduce two new assumptions (the existence of poltergeists and the tendency of the poltergeist in question to vanish valuable objects) which were not previously established. By contrast, the burglary explanation does not require these additional assumptions, since we already know that burglars exist, and furthermore we already accept that burglars have a natural reason to carry off valuable goods, a reason seems inapplicable to poltergeists. As such, we would say that Occam’s razor leads us to prefer the burglary explanation over the poltergeist explanation, since it requires fewer new assumptions.
It is sometimes said that an explanation with fewer assumptions is ‘simpler’, but this is misleading, for such wording implies that the explanation would also be briefer to state and easier to understand. In fact, many highly successful, parsimonious explanations (such as embodied in the theories of quantum mechanics and general relatively) are both very difficult to understand and complicated to explain. Nevertheless, they require few assumptions and explain a wide range of phenomena, and therefore they are considered to be consistent with Occam’s razor.
Occam’s razor: a readable introduction to Occam’s key idea
What is Ockham’s razor?: brief introductory video
William of Ockham: a more detailed analysis from the Internet Encyclopedia of Philosophy