Non-Bonding MOs are orbitals that have essentially the same energy in the molecule as they do in the atomic system. Therefore, they don't contribute to the bond order.
Below is a MO diagram for hydrogen fluoride. It shows the 1s orbital for H as well as the valence orbitals for F. The bonding MO is formed from a combination of the 1s on H and a 2p orbital on F. However there are several MOs (in the middle) that are the same as AO on F. You can see there is one that is identical to the 2s orbital and two other that are the same as the 2p on F. In the diagram, these orbitals are filled, but they don't contribute to the bond order. We can think of them as essentially the lone pairs we would get from the Lewis dot structure.