A normal is the direction a polygon's main surface faces.
In displaying 3D models, rendering out geometry can be expensive, especially if that geometry is never seen by the viewer. For example, a box or sphere, unless there are holes in the geometry, we'll never see the surface of the interior. To reduce the impact of rendering this unseen geometry, a technique called back-face culling is used where polygons whose normal is not pointing towards the camera are not rendered by the engine, speeding up the render process.
Just about all 3D games utilize back-face culling because of the rendering speed increase, allowing for more and higher poly models to be displayed on the screen at once.
Of course, if you are modeling something and wish to have the opposite side be shown, you'd have to duplicate the face and flip the normal's direction.