A nap was a short period of rest.
Enarans had the custom of taking a nap after a large meal without the use of tables and chairs. (VOY: "Remember")
In 2151, Jonathan Archer ordered Charles Tucker III to take a nap to ease his discomfiture inside a Xyrillian ship's decompression chamber. (ENT: "Unexpected")
In 2269, after unknowingly being knocked out by the phony Carter Winston (actually a Vendorian, Leonard McCoy attributed his temporary loss of consciousness to having "taken a little nap". Spock dismissed this explanation, saying, "Doctor, you are a man of curious habits, but I have never known you to nap on the laboratory floor". (TAS: "The Survivor")
In 2270, Montgomery Scott likened shutting down the USS Enterprise's computer to putting her down for a nap. (TAS: "The Practical Joker")
In 2365, William T. Riker ordered Miles O'Brien to take a nap as he, Riker, beamed Data down to Drema IV. O'Brien agreed to "doze off." (TNG: "Pen Pals")
Soon after, Riker expressed his hope that the USS Enterprise-D could discover the IKS T'Ong before its Klingon occupants emerged from their 75-year nap. (TNG: "The Emissary")
In the mirror universe in 2370, Benjamin Sisko told Kira Nerys her efforts to get him to stop Elim Garak's assassination plot were disturbing his nap. (DS9: "Crossover")
In 2371, Rom took a nap after breaking up an argument between Quark and Ishka. (DS9: "Family Business")
In 2373, after Tova Veer's capture aboard the USS Voyager, The Doctor described him as napping in sickbay. (VOY: "Distant Origin")
In 2374, Keevan took a nap aboard Brunt's shuttle just as he and his Ferengi escorts departed Deep Space 9 for Empok Nor. (DS9: "The Magnificent Ferengi")
In 2375, Joseph Sisko took a nap in a runabout soon after departing Earth for Tyree. (DS9: "Shadows and Symbols")
In 2401, Worf fell asleep on the bridge of the USS Enterprise-D from exhaustion, following the events of Frontier Day and the destruction of the Borg Queen's cube. (PIC: "The Last Generation")