This is another logical “principle” to add to Occam’s Razor. The two may seem quite similar, but this is the broader category. Occam’s Razor is a single principle whereas rationalism is an entire field of study in epistemology (the philosophy of knowledge). Rationalism is often associated with the introduction of mathematical models into philosophy, and the pioneers in this approach were Rene Descartes, Baruch Spinoza, and Gottfried Leibniz. You should have heard of at least one of those three philosophers as they are quite famous.
Rationalism is any view appealing to reason as its source of justification. That means that our knowledge can be developed a priori (existing in the mind, independent of experience) through reason. This is arguably the opposite position of empiricism, which holds that all knowledge must come from experience.
For example, I can reasonably argue something predicated on the assumption that this doesn’t exist:
I wouldn’t be required to disprove the existence of the image above because reason dictates that it doesn’t exist. If you want to get more technical, you’d be very hard put equating the mathematical probability of the reality of the image above (hence, it is irrational). This is a bottom up approach similar to the one in Occam’s Razor. Unfortunately, the boundaries reason are often blurred by subjective experience and external teachings, which is why the introduction of mathematics into reasoning was so ground-breaking.
Because rationalism allows for a priori knowledge, it extends our understanding of everything, and provides a logical basis for the understanding of much deeper things. Because empiricism postulates that knowledge can only come from sensory experience, we would have no logical basis for undertaking any work based on the work of others (because we did not experience the thing ourselves), and thus we would have no basis for any advanced science at all. Rationalism essentially broadens the mind by allowing for a logical process by which we can determine “fact” – where fact is the most reasonable explanation. At this point, I should mention that 100% certainty in anything is impossible, so our world operates on a basis of highest probability (so we say that it is a fact if I drop a ball, it will fall to the floor, but there’s actually a tiny probability that a gravitational anomaly would suck the ball up into space at the speed of light).
So here’s the crux of the matter: arguments based on that tiny possibility that something might exist are irrational (and thus illogical) because rational conclusions are based on the most reasonable, mathematically reconcilable answer. If we link this to methodological naturalism, we come to the conclusion that the most logical answer is the simplest one that can describe the given phenomenon.