The Hill sphere applies to objects such as planets that (1) are in orbit around a more massive object, and (2) are massive enough themselves that smaller objects can be in orbit around it. For a planet, the Hill sphere is the imaginary sphere within which a satellite or moon can be in orbit around the planet, and outside of which the Sun or star's gravity prevents the smaller body from orbiting the planet. In other words, the radius of the Hill sphere is the maximum distance a satellite can be from a planet and still orbit the planet.
As an example, since the Moon orbits Earth it must lie within Earth's Hill sphere. However, if the Moon were far enough away from Earth -- outside Earth's Hill sphere -- it would orbit the Sun rather than Earth. The gravitational force from Earth must dominate that of the Sun in order for a satellite to orbit Earth, which only happens if the satellite is close enough to Earth.