Define outflanking

In this exceersice: https://www.chess.com/lessons/view/328

Once the black king reaches h8, white can being outflanking. A few moves later (10. Kh4), white outflanks again despite black being able to take the diagonal opposition. But suddenly this is not so bad. If I would have done this two moves earlier, blacks diagonal opposition would have mattered. It's so confusing.

What is the definition of outflanking in this case?

Yeah, I've never seen it explained very well.

The way I would explain the basic idea is that opposition only lets you zone out the enemy king along a file or rank... not both.

So when you "outflank" you're letting the enemy king take opposition (if he wants it) but it can only block you out along (in this case) a file. Since your goal is to touch either f8 or h8 blocking you out along the g file doesn't make any difference.

Black to move, white has direct opposition
The white king is blocking the black king along the rank, but black can visit any file he wants

Black to move, white has distant opposition.
White can prevent the black king from coming into the bottom right quadrant, but distant opposition can't prevent the black king from touching any of the 4 edges of the board (a1-a8, a8-h8, h8-h1, h1-a1)

So in other words, you give up your direct opposition when it creates a file in between the kings... in other words you let your opponent take opposition, but only when it's distant opposition.

(distant opposition can be noticed when the 4 corners of the box the king's make all have the same color square).

In my 2nd diagram you can tell it's distant opposition because c2, e2, c6, and e6 are all light squares.

The main lesson, IMO, is that distant opposition isn't (for lack of a better word) as powerful.

In many practical endgames, since there are often a lot of pawns blocking king paths, there's no difference between distant and direct opposition, the only thing that matters is that you keep it (if it's keeping the enemy king out).

(In some cases it's actually the side who doesn't have opposition that wins )

In any case, I've never won a game with outflanking... and I've never even noticed an opportunity for it. Again I think the main lesson is simply that distant opposition isn't as powerful as direct opposition when the board is very open. Anyway, to solve puzzles like that, instead of looking for opportunities to "outflank" look for opportunities to give up opposition in a way that only gives your opponent distant opposition.