The Full Form of CATV is‍ Community Antenna Television,

Cable television, generally, any system that distributes television signals by means of coaxial or fibre-optic cables. The term also includes systems that distribute signals solely via satellite. Cable-television systems originated in the United States in the late 1940s and were designed to improve reception of commercial network broadcasts in remote and hilly areas. During the 1960s they were introduced in many large metropolitan areas where local television reception is degraded by the reflection of signals from tall buildings. Commonly known as community antenna television (CATV), these cable systems use a “community antenna” to receive broadcast signals (often from communications satellites), which they then retransmit via cables to homes and establishments in the local area subscribing to the service. Subscribers pay a specified monthly service charge in addition to an initial installation fee.