Great question!  I suppose it differs a great deal from forum to forum, but generally when you have sufficient ongoing activity without having to participate yourself.  That might be a very general working definition of "active forum".   And, of course, active does not mean growing.

There is not really a right answer or a wrong answer, but the general way to look at it is once there are regular posts on your site each day when you are not there and the site has a general increase in posts daily.