Kepler separately observed that the planets follow nearly elliptical orbits around the sun. Then Newton showed that both of these laws could be derived as corollaries from his universal law of gravitation. Once this was shown, it was preferable to adopt Newton's unified theory, rather than the combination of Galileo's and Kepler's. In other words, this rule tells us to assume only what we need to assume for our observations to make sense. Once Newton's assumptions are shown to account for both astronomy and mechanics, Kepler's and Galileo's assumptions become redundant and, the principle tells us, should be discarded.
Atheists often use a similar argument to undermine theism.
God was as good an explanation for man's existence as any, they say, until Darwin showed that the fundamental laws of life could account for our evolution. If two decision rules classify the existing data equally well, the simpler one is more likely to classify future data correctly. Given a simple decision rule A, and a much more complex rule B which classifies the existing data only slightly better than A, A is likely to classify future data better than B. Both of these interpretations are really just special cases following from a more primitive claim, which holds that when assessing the likelihood of future success of different classifiers, we should consider not only their performance on existing data but also their relative simplicities. Simpler classifiers are more likely to be correct. This is because we believe the smooth shape of B probably reflects some reliable property of the data, whereas the squiggles of C depend only on random noise in the existing sample.