Carnival was a traditional Earth celebration still celebrated during the 24th century.
In 2365, a holoprogram available to crewmembers of the USS Enterprise-D was "Carnival Celebration – Rio de Janeiro, Earth". The program, with a code list number of 05-865, was listed in the exercise menu. (TNG: "The Emissary", okudagram)
In 2373, Enrique Muniz, who was in delirium shortly before his death, mistook the Dominion's ultritium concussion shell bombardment of the ship he and others were trapped in on Torga IV, as a fireworks display like those of the carnival he had attended as a youth. (DS9: "The Ship")
Carnival was associated with Christianity.
Carnival could also refer to a traveling performance. In a deleted scene from "The Measure Of A Man", Bruce Maddox crashed the going-away party for Lieutenant Commander Data, which had been precipitated by Data's resignation from Starfleet due to Maddox's demand that he submit to his project, which would involve disassembling him. Maddox asked what he intended to do after leaving Starfleet and he suggested that he might try teaching, that he had already had some success with it. At this, Maddox stated that he had a better idea: carnival work, that Data could be billed as the "Walking Encyclopedia, ask him any question."
Carnival could also refer to a traveling performance. In a deleted scene from "The Measure Of A Man", Bruce Maddox crashed the going-away party for Lieutenant Commander Data, which had been precipitated by Data's resignation from Starfleet due to Maddox's demand that he submit to his project, which would involve disassembling him. Maddox asked what he intended to do after leaving Starfleet and he suggested that he might try teaching, that he had already had some success with it. At this, Maddox stated that he had a better idea: carnival work, that Data could be billed as the "Walking Encyclopedia, ask him any question."