Bond Order

Electrons in bonding molecular orbitals stabilize the molecule.
Electrons in antibonding molecular orbitals destabilize the molecule.

A bond forms only if the bonded atoms are more stable than the separated atoms. Therefore for a molecule to exist there must be more electrons in its bonding molecular orbitals than in its antibonding molecular orbitals.

The net number of bonding electrons for a particular species equals the number of electrons occupying bonding orbitals minus the number of electrons occupying antibonding orbitals.

The bond order is the number of net bonding electrons divided by two because each bond involves an electron pair. Hydrogen (H2) has two electrons in a bonding molecular orbital and none in antibonding orbitals; therefore the bond order in H2 is 1.
 
If the bond order is 0, no bond forms.
A bond order of 1 corresponds to a single bond, 2 to a double bond, etc.
Bond orders can also be fractional (½, 1½).