In this position White cannot play at A, because this point has no liberties.

Here, the two black stones at the bottom are in atari. Atari means that the stones can be taken out on the next move.

In this case, the two black stones are captured by White 1. White can play here because Black was in atari and White gained liberties by capturing.

This is the result.

These eight white stones are connected and have one point of territory. Black cannot play in the center of this shape right now, because a stone there would just be taken out.

But if Black blocks all the outside liberties of the white stones, white will be in atari.

Now Black can play at 1 and take out all the white stones. Black can't play at 1 if White has even one liberty on the outside, because White would not be in atari.

This is the result.