Resonance frequencies are the natural frequencies at which it is easiest to get an object to vibrate. While setting up vibrations at other frequencies is possible, they require much more energy and constant input to maintain than a resonance frequency. Most objects have several resonance frequencies, and this property must be taken into account because of their positive, as with musical instruments, or negative, as with bridges, effects.
Musical instruments make great use of resonance frequencies. The strings of stringed instruments, for instance, vibrate at their resonance frequencies when plucked or struck, and their vibrations against the surrounding air produce sound. For horns and similar instruments, the resonant frequency is actually in the column of air contained in the instrument.
While resonant frequencies are most often applied to vibrations, they are also related to other sorts of natural frequencies, all based on the physical structure of an object. For instance, a swing is a sort of pendulum, and all pendulums have a natural frequency. That is, any pendulum has a natural number of swings for any period of time, and faster movement of the pendulum tends to increase the length of its arc, rather than the frequency of its swings.