This read-only integer (a hop count, despite the source description's spelling 'hopes') determines how many more bridges the BPDU information originated by this bridge on this MSTP instance can still traverse before being discarded. An admin cares because it reveals how close a given switch is to the edge of the MST region in terms of hop count. For example, seeing this value drop to a very low number on an edge switch would indicate it is near the maximum allowed hop count from the regional root.