Satellites stay in orbit due to the balance of two factors:
Satellites never fall into the Earth this because Earth is round and curves. The Earth curves approximately 5 meters downward for every 8000 meters along its horizon. In order for a satellite to successfully orbit the Earth, it must travel a horizontal distance of 8000 meters before falling a vertical distance of 5 meters. Since a horizontally-launched projectile falls a vertical distance of 5 meters in its first second of motion, a orbiting projectile must be launched with a horizontal speed of 8000 m/s. When launched at this speed, the projectile will fall towards the Earth with a trajectory which matches the curvature of the Earth. As such, the projectile will fall around the Earth, always accelerating towards it under the influence of gravity, yet never colliding into it since the Earth is constantly curving at the same rate. Such a projectile is an orbiting satellite.
Man-made satellites circle the Earth in many ways including polar and geostationary orbits.
The satellite in a polar orbit travels over the North and South Poles. A polar orbit may be from several hundred miles to several thousand miles above Earth. This type of satellite circles the Earth approximately 14 times each day. Because the Earth is turning more slowly than the satellite, the satellite gets a slightly different view on every revolution. Over the course of a few days, a satellite in a polar orbit will cover almost all the planet.
The satellite in a high-altitude, geostationary orbit circles the earth once every 24 hours, the same amount of time it takes for the Earth to spin on its axis. The satellite turns eastward (like our Earth) along the Equator. It stays above the same point on Earth all the time. To maintain the same rotational period as the Earth, a satellite in geostationary orbit must be 22,237 miles above the Earth. At this distance, the satellite can view a huge portion of the Earth's surface. Because the high-altitude satellite appears to remain fixed in one position (it's really orbiting at the same rate as the Earth turns), it requires no tracking to receive its downlink signal. That is why when we turn our home satellite dish on to receive the TV signal from a particular geostationary satellite, we don't have to keep jumping up to adjust its position.
One of the advantages of geostationary satellites is that imagery is obtained and displayed every 30 minutes, compared to imagery transmitted by polar orbiting platforms taken every 6-12 hours.