Having a high heat side and a low heat side allows you to first perform a quick sear of the meat before transferring to lower heat to finish the job. A 2-4 minute sear on each side gives the steak a crispy crust and those restaurant-style grill marks.
Once seared, transfer the steaks to the low-medium heat portion of the grill. Cooking on lower heat allows the heat to penetrate to the middle of the steak without overcooking the outside. This is especially true for thicker cuts of filet mignon.