Ko Lock
For White to play in reply to Black's cut here is a standard piece of shape. White has a good reply to Black a atari.
White plays relying on being able to capture at a in sente, forcing Black b. Since there are proverbially no ko threats in the opening, White's plan will very often work and build influence.
Therefore Black usually[1] extends to (or a - the choice isn't straightforward):
next leaves White's marked stone on a good point for shape.
Bildstein: But what is ko lock? Six good and six bad shapes says it is one of the six 'famous good shapes'. This page gives an example, and I can follow the logic of the example to see why it is reasonable play, but I can't tell what it's getting at more generally.
kokiri - in the example, white denies black access to the centre of the board by setting up the ko shape. I think this act of locking black into the side is the point, so white is unworried about winning the ko
This tactic is as old as the hills; but the 'ko lock' name goes back to Victor Chow, a Chinese amateur now in South Africa.
[1] Actually it seems that the atari is also current in pro games, while the extension to a isn't.
TDerz Isn't there an Ishida game (1992 Honinbo) where one player plays the tesuji 3 times, the other stubbornly captures three times the stone?