In a post Terence Tao explained a very nice way to think about convolution and noted that "one should try to use physical intuition to model mathematical concepts whenever one can". I found this very interesting and wondered if math.stackexchange is aware of some other neat examples [Edit attempting to make the question less ambiguous] that perhaps aren't as well known as they should be.
This is a subjective question, but I consider it relevant to this site since [Edit taking note of GPerez's remark] for certain concepts one rarely finds these kind of things in a textbook.