A cycle is a unit of time used by several species.
One Romulan cycle is approximately equivalent to no more than 29.35 Earth minutes. A Romulan officer noted they had no motion on their sensors for twenty cycles. James T. Kirk had also noted in a log that the USS Enterprise had been motionless for 9 hours and 47 minutes. (TOS: "Balance of Terror")
An Argrathi cycle is equivalent to one Earth year. The crime of espionage required a minimum of fifteen cycles of correction on Argratha, and Miles O'Brien served 20 cycles, the equivalent of twenty Earth years (though his entire imprisonment was actually an implanted memory). (DS9: "Hard Time")