Normal force is the force that the ground (or any surface) pushes back up with. If there was no normal force, you'd be slowly seeping into the ground.
On a flat surface, the normal force of an object is .
On an inclined plane, the normal force is reduced by the angle, and the normal force is .
Note that on a flat surface, would be 0, and so would be 1. So the two equations are equal.