What does an air gap within the subject magnets mean?

An "air gap" is a non-magnetic material located between a magnet and an attracted object, or between two magnets that attract each other.
An air gap is best described as a break in the magnetic circuit through which magnetism must jump to continue a circuit between the north and south poles. The introduction of an air gap weakens the magnetic hold.
An air gap can be the air itself or a solid, non-magnetically conductive non-ferrous material such as wood, plastic or aluminum. It can also be a thickness of paint or a very uneven surface.