A cycle is a group of things that happen one after another, again and again, or over and over, as if those things are going around and around in a circle.
And when you cycle through things, you go through them, one by one, maybe forever, as if you're going in a circle.
For example, the seasons of the year are a cycle. That is, the seasons cycle: they change from one to the next over time, again and again. We cycle through spring, summer, fall, and winter; spring, summer, fall, and winter; spring, summer, fall, and winter... You get the idea!
You can think of your days and nights as a cycle, too. Every day, you cycle among activities, going from sleeping to eating to playing to working and back to sleeping again. You do those things over and over, day after day.
Lastly, let's think about how the word "cycle" appears in other words. When you look at a bicycle, and you watch the wheels go around and around, you can see how the movement of the wheels is circular, like a cycle is circular. In fact, the word "cycle" is very closely related to the word "circle"—and to words like "bicycle,"