The great thing about stops is that they give us a way to directly compare shutter speed, aperture diameter, and ISO speed. This means that we can easily swap these three components about while keeping the overall exposure the same.
Let's say you're shooting a scene using a shutter speed of 1/60 of a second, an aperture of f/8, and an ISO of 200. You find that while the scene is well exposed, your subject is turning out a bit blurry, so you decide to increase the shutter speed to 1/120 of a second.
This change of 1 stop will result in the next photo coming out dark, because you're now letting in half the total light as before. In order to correct this, you need to reclaim that 1 stop reduction from somewhere else. Now that we have a way of comparing settings, this is simple.
You could open the aperture wider to let in more light - moving from f/8 to f/5.6 is an increase of 1 stop, so we've got back to our original exposure. Alternatively you could double the ISO speed from 200 to 400, again resulting in a 1 stop increase.
As you can see, stops are a really easy way of adjusting our camera's settings while making sure we don't ruin the photo's overall exposure.