Why do the burners on my stove turn on and off while in use?
The "burners" on an electric range have TWO settings - off and on. There is no in between. So they turn on and off to maintain a goal.

With the burner set to high, normally they stay on almost all the time, heating the pot on top of it to boil water. With the heat control set to an intermediate value, the burner will kick on and off repeatedly to maintain a goal temperature. However, if you leave a pot off of the burner, they will overheat if they stay on permanently. The temperature sensor recognizes this fact, and that there is no need to leave the burner on.

All of this is different for a gas range, where it is the amount of gas that is fed to the burner to control the heat.

Note that an electric range will cook more slowly than a gas range. So you may think the stove is not working properly, when it actually is working as it is designed. One other important point - a smooth top range like this cooks most efficiently with flat bottomed pots. You need good contact over the bottoms to get good heat transfer, and good heat transfer is essential for cooking. Check this fact by taking one of your pots and hold a ruler across the diameter (underneath the pot). Or take the pot and touch the edge of your counter top. Sight along that straight edge. Most pots tend to have a bit of a dish to them, so the center of the pot may stand off by as much as 1/4 inch. Those pots will perform poorly. (Sorry, but they will.)

That concave pot bottom is fine for a gas range. But it will hurt you with a smooth top electric range.