Property was anything which was owned, such as land.
During the trial held to determine Data's status as a person or if he were the property of Starfleet in 2365, Captain Picard argued that self-awareness was a key ingredient of one being an individual. Commander Bruce Maddox indicated that what made someone self-aware was that they were conscious of their existence and actions, that was, "you are aware of yourself and your own ego." When Picard turned to Data and inquired directly, "what are you doing now?" Data responded that he was "taking part in a legal hearing to determine my rights and status. Am I a person or property?" When Picard inquired whether or not Data knew what was at stake, Data replied, "my right to choose. Perhaps my very life." Picard echoed Data's response, "'My rights.' 'My status.' 'My right to choose.' 'My life.' It seems reasonably self-aware to me." (TNG: "The Measure Of A Man")