Bond order is the number of bonds between a pair of atoms. For example in nitrogen N≡N the bond order is 3, in acetylene H−C≡C−H the bond order between the two carbon atoms is 3 and the C−H bond order is 1. Bond order gives an indication to the stability of a bond. In a more advanced context, bond order need not be an integer. A good example of this is bonds between carbon in the molecule benzene where the delocalized molecular orbitals contain 6 pi electrons over six carbons essentially yielding half a pi bond. Together with the sigma bond the bond order is 1.5. Furthermore bond orders of 1.1 for example can arise under complex scenarios and essentially refer to bond strength relative to bonds with order 1.
In molecular orbital theory bond order is also defined as the difference, divided by two, between the number of bonding electrons and the number of antibonding electrons per the equation below. This often but not always yields the same result. Bond order is also an index of bond strength and is also used extensively in valence bond theory.