In The Martian, "sol" is short for "solar day," and is a term used by planetary astronomers to describe the duration of a solar day on Mars. A sol lasts for 24 hours, 39 minutes, and 35.244 seconds, slightly longer than the equivalent solar day on Earth.
Watney spends a lot of time constructing solar panels as a way of keeping to Martian time instead of the Earth time used by mission control. Mindy Park, a NASA employee who works at Satellite Control, monitors his movements, arranging her schedule according to what she calls "Watney time," i.e. a Martian solar day. This involves putting foil over her windows so she can sleep during the day—which is Watney's night—and watching him on the satellite feed during the night—which is Watney's day.