A resonance is a concept of great importance in various physical theories, from classical wave propagation to high-energy particle scattering. But resonances are also fascinating quantities in a purely mathematical context. For example, the Prime Number Theorem could be seen as a result on the distribution of resonances associated to a particular surface. This talk will explain in very basic terms what a resonance is and then give some examples to illustrate the interesting connections between resonances and various topics in geometry and number theory.