The mode shows you the buckled shape. It is important because it shows you which way the structure moves.

A negative sign on the load multiplier simply means the structure will buckle when the load is applied in the opposite direction.

Sometimes you have no interest in buckling under loads in the opposite direction because that could never happen. In those cases, you can instruct the solver to exclude negative load multipliers.  In other cases, you may be interested in the smallest load multiplier both positive and negative.