Points of this type are often called focal points. The idea is that on the boundary of Black's framework and White's framework, a play by Black will improve Black's framework and at the same time reduce or threaten White's framework.
Therefore these points are big because they are double-purpose plays. They are often played in the opening as secondary big points (and are frequently the solution to whole-board problems with quiet positions).
See Strong Groups for an example and discussion.
Game played 1927-11-25: Go Seigen as Black played at 1 in reply to the marked white stone blocking off the side. This is considered both excellent timing, and a clear-sighted focal play (Black has no need to invade on the right).
Quite a move for a thirteen-year-old to come up with. Go Seigen was still in China at the time.
 Comment: That seems strange to me. There is nothing focal about such points. They are not at any focus, but at the frontier between moyos. I would call them frontier points or boundary points.
Bill: (Much later.) I have found a term I like better, contact point (of two moyo). And I do not think that such points have sector lines converging on them. The example certainly does not.
Bruce Wilcox I prefer the term "pivot point" as they are a fulcrum, shifting the balance of growth and withering of two moyos.