A Satellite is any object that orbits another object (which is known as its primary). All masses that are part of the solar system, including the Earth, are satellites either of the Sun, or satellites of those objects, such as the Moon.
It is not always a simple matter to decide which is the 'satellite' in a pair of bodies. Because all objects exert gravity, the motion of the primary object is also affected by the satellite. If two objects are sufficiently similar in mass, they are generally referred to as a binary system rather than a primary object and satellite; an extreme example is the 'double asteroid' 90 Antiope. The general criterion for an object to be a satellite is that the center of mass of the two objects is inside the primary object.
In popular usage, the term satellite normally refers to an artificial satellite, which would be a man-made object that orbits the Earth (or another body). However, scientists may also use the term to refer to natural satellites, or moons. In general word usage, "natural satellite" is the term used to refer to moons.