Rule of capture

Before the play  

The white stone is almost surrounded. It is adjacent to only one empty point, shown by the square. (An empty point adjacent to a stone or connected group of stones is called a liberty.) It is not adjacent to other nearby points, shown by circles.

Black captures  

Black's move surrounds the white stone completely.

After the play  

Black's move occupies the last liberty of the white stone, thus capturing it and removing it from the board.

(Example 2)

After the play  

The 3 white stones are connected along the lines of the board, and stand or fall together.

Blacks' move occupies their last liberty and removes them from the board, capturing them.

(Example 3)

After the play  

A play can also surround different stones at the same time even if not all of them are connected along lines. Black's move captures the surrounded five white stones. For this Black occupies the last liberty of the four white stones at the top which is also the last liberty of the one white stone in the middle. All the white stones without liberties are captured and thus are removed.

(Example 4)

After the play  

The White play occupies the last liberty of the two black stones, and removes them.

It does not matter that temporarily a white stone does not have a liberty; after execution of the White play, all stones on the board have at least one liberty again.