Shortage of liberties is the theme here.
is the key,
has to prevent
from escaping. After
, black can't approach from either side.
Alternatively,
at 'a' also works.
in the previous diagram is better, because with ouside help, black can try to escape like this.
After , the best white can do is getting a ko with x or y.
It is important to notice where the outside liberties are. Let's look at this related problem.