A satellite is any small object that stays in motion around another. Moons are satellites of planets. The Moon is a satellite of the Earth. Planets are satellites of stars. The Earth is a satellite of the Sun.
We normally think of satellites, however, as objects sent up from the Earth's surface and put into a low orbit around the Earth. They are used for seeing into space, seeing the Earth's surface, passing messages (communications satellites) and so on. There are thousands above us now, but the first one was the Soviet Union's Sputnik 1.
Some of these satellites are called geo-stationary satellites. This means they stay still, or 'hover' in one place all of the time. To do this they have to turn at the same time as the Earth. There is a special distance they have to be away from the Earth's surface for this. It is 35,786 km (22,236 mi) above the Earth's Equator. Communications satellites and weather satellites are placed in geo-stationary orbits, so that the ground station dishes that send and receive signals do not have to rotate to track them.
Another useful orbit is called a geo-synchronous orbit. In this case the satellite in geo-synchronous orbit returns to the same point in the sky at the same time each day. The reason these satellites are used is because geo-stationary satellites have to be fixed over the Equator and so can only see part of the Earth's surface. This means they are not useful to give a complete communications coverage of the Earth. Most communications satellites are geo-synchronous, with tracking dishes on the ground.
Satnav systems (the ones we use in our automobiles) use something different. They get a complete world-wide coverage by using groups of 20–30 medium Earth orbit satellites. The United States' Global Positioning System (GPS) consists of about 32 medium Earth orbit satellites.