Newton's 3rd Law applies to every force. Forces come in pairs, always. Gravitational force occurs when two objects (i.e. a person and the Earth) are in significant proximity to each other. Each feels a force of equal magnitude and opposite direction. The person and the planet are labeled as an "action/reaction pair"
Distance is taken from the displacement between their centers of mass. Any distance will produce a force of universal gravitation, but greater distances will diminish the strength of gravitational forces.
An example of Newton's 3rd law and gravity would be the detection of exoplanets. Planets orbit their star because the star has more mass than they do, but the planet also has mass, so it pulls on the star as well. Because of that, the star will "wobble," and by studying that wobble astronomers can tell if a star has planets and get an idea of how big they are. Basically, the star and the planet are both pulling on each other with an equal amount of force, but because the planet has way less mass, it accelerates much more (Newton's second law) and therefore has the larger orbit of the two.