A satellite dish is another name for a parabolic antenna. The dish shape allows signals hitting anywhere on the dish to be focused in one central location. Exactly at this location there is signal receiving hardware, called a "feedhorn". The structure of a satellite dish allows the antenna to receive signals from very long distances so long as the dish is facing the signal.
Because of there ability to receive signals from long distances, parabolic antennas are ideal for signals from satellites, thus the name "satellite dishes". In recent decades, satellite television has gained in popularity. Along side this growth, came the advent of the mini-dish. These mini-dishes are generally less than 30 inches across and are used in individual homes to receive television signals directly from TV satellites.
There are many uses of satellite dishes beyond receiving TV. Larger satellite dishes are use to send signals to satellites as well. Even larger satellite dishes can be used as telescopes. The largest of dishes are used for receiving signals from distant space, such as the famous Arecibo Observatory in Puerto Rico