The prototype idea is to study the Sun-Earth-Moon system, and determine if it would be possible for the Sun to steal away the Moon from Earth orbit, into solar orbit.
Besides the moon, the satellite is usually a small planetoid, exoplanet, or a spacecraft that is orbiting the earth.
[1] The Laplace sphere is a region around a planet where a satellite would maintain a stable orbit around the planet, rather than being pulled off toward the star, with its greater gravitational force, despite its larger distance.
The 'sphere' region is actually an ellipsoid, specifically a prolate spheroid with its long axis perpendicular to the star-planet orbit.
The derivation eliminates higher-order terms on the assumption that the star's mass is much larger than the planet's, and the planet's mass is much larger than the satellite's.