Ok, Dallas, I will try
to keep Dr. Paul's influence out of this....but I have two of his books and 7 of his speaker tapes, so I may be unconsciously guided by his Spirit
The first thing that comes to mind for me is the 3 A's - Awareness, Acceptance, Action. I have a hard time getting in to Action if I don't first Accept (Own) what's mine (and I can't Accept/Own it if I'm not aware of it). So, to me, Acceptance is knowing that "it is what it is" - taking an objective stock of a situation, defect, whatever it is. Acceptance is, to me, not fighting Reality. Acceptance does not mean Approval.
Even if it is something that I need to change, I have to accept it first. To me, the opposite of acceptance is denial. If I am in denial, I am not going to be able to make any changes.
I once heard someone say "The pain is in the resistence." That was one of the most profound things I heard in recovery. It is only when I resist reality that I hurt. When I am able to Accept life on life's terms, I am at peace.
I doubt any of this ties in with the quote in your post, so let's see if I can get to that. I guess for me, in that regard, acceptance is full integration of the belief. Not in theory, but in reality.