A transponder is a radio system that, upon receiving a coded signal, responds with a radio transmission of its own. The transponder signal identifies the source and may also send other information such as location, heading, local environmental data, etc.
In Star Trek
Star Trek vessels rely heavily on transponder signals to locate and identify other starships. In TNG "The Wounded", for example, Cardassian ships could not locate the Federation starship USS Phoenix -- which was destroying cargo ships in their territory -- until Captain Picard gave them the Phoenix's transponder code.
To the surprise of Cardassian ship commander Gul Macet, the Federation had already broken Cardassian transponder codes and could locate and identify Cardassian ships from a great distance.
Personal communicators also function as transponders, allowing a starship to determine the locations of its personnel who are wearing operational communicators.