The hprof, histogram shows the number of object by class.
is this the total number of object that have ever been allocated during the life of the jvm ?
or is this the number of object where are currently on the heap ?
or is this the number of currently reachable object on the heap ?
It depends. If you're generating dump with "live" (for example
jmap -histo:live PID
) option it's number of reachable objects. In other case it's number of objects currently allocated on heap.