Animation was a filming technique that was designed to give the illusion that cartoons or computer images were in motion.
A number of animated films were mentioned in the Treaty of Armens, such as Akira, Ranma Nibunnoichi, Urusei Yatsura and Rhea Gall Force. (TNG: "The Ensigns of Command")
Circa 2285, a computer animated short film was developed on Regula I to demonstrate the Genesis effect. This was classified information, but James T. Kirk allowed Captain Spock and Doctor Leonard McCoy to view it. Kruge and a few of his crew on his ship also viewed the top secret file. (Star Trek II: The Wrath of Khan; Star Trek III: The Search for Spock)
This same computer animated film was later shown at Starfleet Headquarters as evidence from the Klingon ambassador against James T. Kirk, who he claimed murdered a Klingon crew, and gave this as a reason for his declaration that peace would never come to pass, as long as Kirk is alive. (Star Trek IV: The Voyage Home)
A commercial for Tribbles cereal had live actors as well as a cartoon character. It was an animated tribble riding a skateboard, who then multiplied into three. (ST: "The Trouble with Edward")