Objects in contact generally exert forces on one another. A book rests on a table: the book exerts a downward force on the table, and the table exerts an equal-and-opposite force up on the book. We call this the normal force - "normal" is the technical physics word for perpendicular. The normal force is perpendicular to the interface where the book meets the table.
The normal force is one component of the contact force between objects, the other component being the frictional force. The normal force is usually symbolized by N or FN.
Objects lose contact with one another when the normal force goes to zero.
The normal force is the force that would be measured by a scale placed between the objects in contact.
Your "apparent weight" (how heavy you feel) is directly related to the normal force you are experiencing.