This is the Stage (the white rectangle), where you will be drawing and manipulating imported objects. The gray area is extra space, where you will sometimes store objects off the stage so they can "enter" the stage at some point in your movie. Sliding objects in from the side often gives nicer results than just having them suddenly appear on stage.

Make sure you investigate all the areas of the Flash Interface before you get into the tutorials, we will be referencing these items without all the screenshots later on, so you will move faster if you spend a few extra minutes here.