Plain English Meaning
The aircraft sends its position and flight data automatically, but only to one specific air traffic control facility it has set up a link with — not to everyone nearby.
Full Definition
A surveillance system in which an aircraft automatically transmits position, altitude, and other flight data over a data link to a specific, named recipient — typically an air traffic control facility — under a one-to-one contract between that aircraft and that recipient. Unlike ADS-B, which broadcasts to anyone in range, ADS-A reports are addressed only to the agreed receiving party and are usually used in oceanic and remote airspace where radar coverage is unavailable.