The reason isn't always stated, but if you look for it, often it isn't too hard to find. The same advice applies on a smaller scale, and I think that's what Polya had in mind. Learn the vocabulary. Mathematics obtains much of its power by constructing a very precise vocabulary. When learning new mathematical vocabulary, it's helpful to distinguish between formal and informal definitions.
Informal ones are good for getting a feeling for what the word means.
They help to build up your intuition. Formal definitions are also important for building intuition. Just that working with a formal definition will help you to develop correct mathematical intuition for the concept. They develop it by working with the formal definition. Because formal definitions are precise, they are one of the few places in mathematics where memorization can be useful.