Picture the entry/clearing of a room. Your approach keeps the wall and jamb away from you (anti-Hollywood style), to prevent someone inside the room from grabbing your weapon.
By "slicing the pie", it is meant to move in a determined and continuous arc or line around the entryway with the weapon at, or close to, eye level. As you move in the arc or line "pie shaped" slices are revealed to you and threats assessed and eliminated. With each new "slice" you attempt to expose only your weapon, hand(s) and shooting eye to the scanned area.
By the time you've finished the move/scan/ assess/shoot, you have only the blind spots on either side of the door or behind obstacles/other doors to clear.
Hope this helps.