Handedness was an individual's preference for using one hand over the other.
One's handedness could be determined by an analysis of one's handwriting. In 2369, Data, as Holmes again, attempted to prove that a right-handed murder victim's left-handed brother wrote a suicide note by throwing a box of matches to the man. The accused caught it with his right hand due to a holodeck malfunction. Reginald Barclay asked James Moriarty if he was right or left handed, to which Moriarty replied that he was left-handed. (TNG: "Ship in a Bottle")