Framing was the act of making it appear as though somebody other than the culprit had committed a crime, often murder. Motives for framing someone included revenge and deflection of guilt from the actual party.
One could also be framed for a crime which had not in fact occurred. In 2267, Benjamin Finney framed James T. Kirk for his apparent "death" in order to get revenge on Kirk, whom Finney believed to be responsible for his not being promoted. (TOS: "Court Martial")