When something happens from time to time on an irregular basis, we say it is an occasional occurrence. For example, you might have an occasional lunch with a friend. If your friend ever picked up the bill, maybe it would happen more often.
Occasional is a few steps removed from the Latin cadere, "to fall." So you might think of something occasional as something that happens "to fall" just whenever it happens to fall. Speaking of falling, Voltaire once wrote, "The best government is a benevolent tyranny tempered by an occasional assassination." An occasional election might do in a pinch.