The buckling length is the length that HyperSizer will use when doing a beam buckling analysis. When the finite element model is imported, HyperSizer attempts to determine the appropriate beam buckling length, but sometimes it might get confused depending on your geometry. If it appears that the unsupported length of your beam is different than the 484 mm that HyperSizer calculated, then you can over-ride this value and type in your own value.
The "Length" shown on the Design-To Loads tab is the length obtained by adding the length of every individual beam element together. This length is not used by any analysis, rather it is just used when calculating the total weight of all of your beams by multiplying the beam unit weight (in kg/m) times the beam length (in meters).
A note about beam buckling. The buckling analysis that HyperSizer is performing as the "beam buckling" checks are Euler column buckling checks that are really meant for unsupported beams. If your beam is supported by another structure, for example, your beam is a ringframe or a sparcap, then the beam buckling failure modes are really unnecessary and will cause your beam weights to be over-conservative.