A non-conservative force is a force that doesn't conserve (store/maintain) the energy from the force.
A box at rest on a table doesn't conserve the energy from the normal force the table applies to the box. If you now slide this box across the table, the normal force from your hand, the normal force from the table, the force of air resistance, and the force of friction acting on the box are all non-conservative forces (the energy isn't stored in the object in any of the examples).