I have always heard the term used either in P/K arts as "focus" with a punch or kick. In judo it often is used to mean the decisive moment in osaekomiwaza where tori has achieved control and the time should start. Also in kansetsuwaza, it is the place where the joint is locked and uke can't power out or use the limb, etc. (and of course as you mention in the Kime no kata).
I have always used the term in aikido to mean the joint is locked and along with the rest of the structure associated with the joint lock can't really function to get away. In other words, the decisive point of when the lock is effective. Pain can be there but is not necessary.
I often feel that when someone goes for pain in a lock with me that it gives me "feedback" to know where their center is and can be countered. Sure, it can hurt, but there's a window of opportunity there if you're sensitive to it.