One light day is the distance that light travels in one Earth day, a distance of twenty-four light hours.
In 2265, the USS Enterprise was a few light days away from Delta Vega after it had cleared the galactic barrier. (TOS: "Where No Man Has Gone Before")
In 2267, when Spock requested a leave on Vulcan, the diversion would have caused a loss of 2.8 light days to the course of the Enterprise. (TOS: "Amok Time")