A cycle is a whole-board repetition after an even number of moves (each a play or a pass).
The most prominent members of this club are the trivial cycle and the immediate ko recapture. The latter, of course, is banned by any rule set. Therefore most of us will only experience the trivial cycle in their lifetime.
Note that only even repetitions complete a cycle. The term situational cycle therefore is deprecated — the modifier is superfluous.
Note further that whole-board repetitions after an odd number of moves need a further pass to complete a cycle. The term positional cycle therefore is also deprecated — what is not a cycle, is [a fortiori] not a special kind of cycle.
The former content of this page was adjusted and moved to whole-board repetition. You find all examples there.