There is method java.lang.ThreadGroup.activeGroupCount() returns an estimate of the number of active groups in a thread group. In response to this question, the active thread is defined. But what does active thread group mean?
As you noted, the terminology "active thread group" appears in the javadoc for ThreadGroup::activeGroupCount.
An active thread group is a ThreadGroup containing at least one active thread.
An active thread is one for which Thread::isAlive returns true. In other words, it has been started and has not yet terminated.
Note that thread groups are are only really suitable for debugging; see What is the benefit of ThreadGroup in java over creating separate threads?. For example, the enumerate method has this javadoc caveat:
"Due to the inherent race condition in this method, it is recommended that the method only be used for debugging and monitoring purposes."
This also applies to the "count" methods.