Personal time was any time set aside for pursuing one's personal life or dealing with other matters which needed to be addressed.
As of 2152, Kaitaama spent her personal time with her father's advisors, rather than suitors. (ENT: "Precious Cargo")
In 2367, Jean-Luc Picard granted extra personal time to the crew of USS Enterprise-D after the early completion of their mission at Harrakis V. Tight schedules as of late had curbed such activities. (TNG: "Clues")