Fundamentally, the classical elastic buckling issue could be interpreted as a bifurcation in the solution to the equations of static equilibrium, at which point the singularity of the stiffness matrix is triggered.

In abaqus, for different buckling modes, it corresponds to the possible instability modes of the components. The first few modes would likely to occur since the corresponding load is relatively small.

In reality, a component would “buckle” due to eccentricity and lateral interference. Therefore, these modes would provide indications for the potential buckling shape in real cases. Also, you could introduces these modes as initial imperfections into you model to  simulate an inelastic buckling issue.  

Thanks.

Ke