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.
'a' no longer works because of the liberty at 'x'. It won't be explained here but at 'b' is the killing move for this black group.
This is the original problem, do you see the difference?
Without external liberty:
Life and death problem 001 on Michael Redmond's Go TV
With outside liberty:
Life and death problem 002 on Michael Redmond's Go TV