An audio tape was a type of tape used for audio storage and playback.
In 2267, USS Enterprise First Officer Spock played falsified audio tapes of Captain Kirk from the Starbase 11 Communications Center assigning command of the vessel to Spock. (TOS: "The Menagerie, Part I")
In 2270, Uhura and Sulu thought they heard the sound of someone chuckling in the recreation room. McCoy shrugged it off as one of the audio tapes rewinding. Unbeknownst to them, it was actually the Enterprise's computer laughing. (TAS: "The Practical Joker")