What does non-integer bond order mean?
It is one of the man-made tools to conceptualize the nature of a bond between two atoms, to know if there is a single / double / triple / quadruple *) bond between them, and to account for both electrons involved in bonding / antibonding molecular orbitals.  Because the nature of electrons is neither "true and only" particle, nor wave alone, hence sometimes escaping our day-to-day experience with macroscopic objects.

In addition, rarely you look at the bond order of two atoms in a molecule without keeping in mind the situation with other atoms present in the same molecule, too.

*)  Sorry, I forgot at least the three-centre-two electron bonds in diborane...