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 another example and discussion.
Go Seigen as Black played at 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!
 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.
Patrick Traill (2019-03-12): Perhaps the idea is that they are where conflict is focussed? Chambers Dictionary gives “the point or region of greatest activity or interest” for focus, and this seems to be closest to the Latin meaning of hearth. (This sense is lacking in Wiktionary.) Surprisingly an older, historically ordered edition of Chambers does not give this as the first sense and my OED is too deeply buried for now.
- If this comes to a conclusion, it should be cleaned up and introduced into the article(s) as appropriate
Bill: I may be corrected, but I believe that tennozan is based on the site of a famous battle, and indicates a strategically important point, like the high ground in a battle. It is a more general term than focal point.
Patrick Traill (2020-08-13): Thanks, Bill. It may be more general, but on the other hand, the article Tennozan also tells us that to be tennozan a move has to be able to decide the direction of the game. It would help one understand the distinction if somebody could provide examples of three points/moves which are one, the other and both, with explanations why! I also imagine that “focal point” is of Western origin.
Bill: AFAIK, Patrick, tennouzan is regular Japanese, not go jargon. I would not trust any unsigned material on SL that says otherwise. "Has to be able to decide the direction of the game" sounds like editorializing to me. As for focal point, setten in Japanese means point of contact, which seems reasonable. I would prefer frontier, myself, but point of contact is OK. Now, for a lens that bends light to converge on a point, that is a focal point. It is also a point of contact, but point of contact between moyos is not a focal point, IMHO. I think that focal point is a mistaken translation from long ago.