They are used to listen to many frequencies of radio transmissions. Normal radios are from around 88mHz to 108mHz. Radio scanners have a much greater and diverse range of frequencies. You can typically pick up aircraft, police, and fire transmissions, ham radio conversations, weather reports, ... I almost always use mine to listen to aircraft. I can listen to them talking to each other, talking to air traffic control, etc. You can get them at most large electronics stores. I got mine at Radio Shack, for US$130.
The more you pay, typically the more frequencies you can pick up, more frequencies and be stored, more modes, greater ease of use, and clearer reception.