Asset categories is if the sponsor invested in each asset category at their strategic asset allocation, B/m is the weighted average returns of each b/m chosen to represent the asset class. You can think of the difference like misfit return (it is the return generated because the benchmark does not exactly match the asset class they are trying to replicate).
Finally, allocation effects is the residual, mostly due to cross products of managers doing poorly/well and changing the allocation of the entire portfolio over the measurement period. (but mostly all you need to know is that it is the residual.