The Cycle is the unit of time in the game. Game days correspond to days of their real life (if there is such a thing).
A Cycle lasts 3 hours and there are 8 Cycles in each Earth day. Certain cycles have particular associated events. At the end of Cycle 8, for example, around midnight, certain actions will be reset.
You earn an unspecified number of action points every Cycle depending on various factors.
Your watch is shown in the top-right of the site, and shows how much time remains until the next Cycle.