the 'active' tab looks like it's just a 'most recent change'. maybe the word should just be 'recent' then? the word 'active' to me suggests something more like 'hot'. but then, how is the 'hot' tab sorted? ... and should it be sorted differently?
From this question on SO's Meta:
Active is based on creation / last modified time of any answer or the question itself. So the recently changed questions or new ones are in the active list.
Hot seems to be a mix of how recent the question and how busy it is. (votes, answers, comments etc)
See some of the linked questions from the above to get feel of how this all comes together.
By the way, there's also a newest tab that sorts by the time the question was asked.