Questions regarding the phenomena by which the ratio of the orbital periods of two (or more) bodies is a fraction of small integers, because of the gravitational interactions between them.
An orbital resonance is a situation where the ratio between the orbital periods of two bodies in orbit around a common barycenter is a fraction of small integers. In this configuration, the orbiting bodies "push" each other periodically, like pushing someone on a swing.
One well-known example of an orbital resonance is the case of Io, Europa and Ganymede which are in a stable orbital resonance, with orbital periods that follow the ratio 1:2:4. This was also the first orbital resonance to be discovered.
Orbital resonance drives the formation of arms in spiral galaxies, through Lindblad resonance.