Normal Force is the force that surfaces exert to prevent solid objects from passing through each other.
Normal force is a contact force. If two surfaces are not in contact, they can’t exert a normal force on each other. For example, the surfaces of a table and a box cannot exert normal forces on each other if they are not in contact.
However, when two surfaces are in contact (e.g. a box and a table) they exert a normal force on each other, perpendicular to the contacting surfaces. This normal force will be as large as necessary to prevent the surfaces from penetrating each other.