A Cycle is a measurement of time used on the Grid. Interpreting the dialogue of TRON: Legacy, a cycle is a fair amount of time (likely more then a day, maybe more equivalent to a year or season).
Kevin Flynn mentions that a millicycle is about 8 hours. If the usage follows the International Standard Organization's use of the prefix "milli" that would mean that a cycle is about 8,000 hours (for comparison an Earthly year, by the Gregorian calendar, is about 8,760 hours (twenty-four times three-hundred-and-sixty-five)). But that measure is speculative and non-canonical.
The specially released TRON: Legacy tie-in magazine guide includes a timeline of the Grid, explaining that time moves faster in the system because its only limit is the speed at which electrons can move in circuitry. The guide states that one year in the real world equals about 50 Cycles in the Grid, which would mean that Kevin Flynn was trapped inside the Grid for roughly 1,000 years from his viewpoint. This would seem to be confirmed within the movie itself by Castor's line that Clu had been trying to obtain Kevin Flynn's Identity Disc for about 1,000 cycles.