The eye at a is already secured. White needs to make another in the space around b. First, immediate capture is insufficient - makes the eye false.
Second, capturing two stones by and is also insufficient - and throw-in at again makes the eye false.
So White chases Black longer with and then ! threatens to capture three to make an eye, forcing Black to capture with . (Note: at a is an unnecessary sacrifice, though it lives similarly.)
After , Black can't connect at because of White's cut at , capturing all six in connect-and-die. This trick works only near the corner - if the whole position is moved one or more lines to the right, White is dead.