"Rest and relaxation. You know, down time. When we're not working."
"You sleep a full third of your rotation. You rest and relax while you are awake. The Alpha Quadrant has far too much "down" time."
R&R was abbreviated military parlance with several origins, such as rest and relaxation, rest and recreation, or rest and rehabilitation, all pertaining to a short vacation given to members of a military force. Some atypical synonymous terms include down time and relief and diversion.
While preparing a survey on an uninhabited planet, Jonathan Archer suggested he and Tucker could spend some R&R after completing the mission. (ENT: "The Catwalk")
In 2154, Jonathan Archer suggested that Hoshi Sato take some R&R in Norway or Canada after the Xindi crisis had been averted. (ENT: "Zero Hour")
In 2268, the USS Enterprise approached Starbase 6 for much needed rest and recreation. According to Captain James T. Kirk, the crew had performed excellently but was exhausted. Kirk too looked forward to a nice period of rest on some lovely planet. (TOS: "The Immunity Syndrome")
Later that year in a medical log, Doctor Leonard McCoy attributed Captain Kirk's indications of increasing tension and emotional stress to possibly being on patrol too long without relief and diversion. (TOS: "The Enterprise Incident")
The Starfleet crew of Deep Space 9 often took R&R in Quark's. The concept was alien to Tosk – as he observed Humans slept a full third of a day and spent their awake time resting and relaxing – he felt that the Alpha Quadrant had too much "down" time. (DS9: "Captive Pursuit")
After he was assigned to the former Federation colonies in the Demilitarized Zone, Calvin Hudson had hoped to spend some R&R time with his old friend Benjamin Sisko, but, as Sisko himself pointed out, "who's got R&R time?" (DS9: "The Maquis, Part I")
In 2374, Admiral William Ross was motivated to spend his next R&R on Bajor, following Benjamin Sisko's descriptions of the planet's beauty. (DS9: "Favor the Bold")
After talking to many people on the USS Defiant later that year, Captain Lisa Cusak suggested that the crew could use some R&R. (DS9: "The Sound of Her Voice")
In 2375, after Rom told him Grand Nagus Zek was missing, Quark suggested that he may be having "a little rest and relaxation" on Risa. (DS9: "The Emperor's New Cloak")