A diet card was a set of instructions provided by a Starfleet vessel's chief medical officer, specifying nutritional requirements for individual crewmembers in the 23rd century.
In 2266, Doctor McCoy changed Captain Kirk's diet card to include dietary salad, as Kirk's weight had gone up a bit since his most recent physical. (TOS: "The Corbomite Maneuver")
Later that year, Lieutenant junior grade Joe Tormolen used a diet card to obtain a tray of food from a food synthesizer in one of the USS Enterprise's recreation rooms. (TOS: "The Naked Time")
The diet card in "The Naked Time" isn't identified as such on screen; its designation as a "diet card" comes from the episode's final draft script.