Although objects have a fundamental frequency, some objects have other frequencies at which they can vibrate at. We typically hear the lowest natural vibrating frequency, and the other (higher) ones are called overtones. They are part of what give different instruments their characteristic sounds.

This concept is easiest to visualize with a vibrating string. When you pluck a string, it does not result in just a single standing wave. You actually get a bunch of different standing waves that are overlapping each other. Each standing wave creates its own tone and you hear the overlapping of all of these tones. (Reality is a bit more complicated, as you’re also hearing vibrations in the structure of the instrument.)