What does this equation mean?

Because [X,Y] is itself proportional to the identity, it commutes with both X and Y , so every higher term in the Baker–Campbell–Hausdorff expansion of $e^X$$e^Y$$e^{-X}$$e^{-Y}$ vanishes identically, at all orders, with no small-loop approximation required: $T(\mathbf b)\,G(\mathbf v)\,T(-\mathbf b)\,G(-\mathbf v)=e^{[X,Y]}=\exp\!\left(\frac{im}{\hbar}\,\mathbf b\cdot\mathbf v\right)\mathbb 1$. The structure is the same one that makes an Aharonov–Bohm phase or a Berry-phase holonomy nonzero: a closed path in a classical parameter space picks up a phase set by a curvature that lives on that space, even though nothing classical distinguishes the endpoint from the start. Here the “curvature” is the commutator [$K_i$,$P_j$] itself, and the “charge” that couples to it is mass. The analogy is a guide to intuition, not a claim of identity — there is no background field on the group manifold in the electromagnetic sense, only the algebra’s own structure constants — but it explains why the effect survives however the loop’s interior path is traced, so long as the net translation and net boost at the end match: like a Wilson loop, the phase depends on the loop’s declared endpoints in group-parameter space, not on the particular way the apparatus was walked between them.