The verb “reign” means to exert legal authority over something — essentially, “to wield sovereignty” — so for example reigning over something would be enforcing your rule over it. For another example, whoever wins the US presidential election this November will reign as the next president.
The striped ropes you see in this picture:
are called “reins.” They’re used for controlling horses and other broken in livestock, hence phrases like “free rein,” which is what it’s called when you let those ropes go slack and let the animal walk of its own accord. Another phrase with which you might be familiar is “rein in.” When you rein in a horse, you pull on those ropes to bring it to a halt.
Always remember, it’s a wasted day if you haven’t learned something new.