$$B Black captures the white stones
$$ | . . . . . . .
$$ | X X X X X . .
$$ | O O O O X . .
$$ | O 1 O O X . .
$$ ---------------
- Click Here To Show Diagram Code
[go]$$B Black captures the white stones
$$ | . . . . . . .
$$ | X X X X X . .
$$ | O O O O X . .
$$ | O 1 O O X . .
$$ ---------------[/go]
In this diagram,

removes the last liberty of these 7 white stones. By the rule of capture, the white stones are removed from the board.
This is what we mean by Black
captures the white stones.
$$B Black kills White
$$ | . . . . . . .
$$ | X X X X X . .
$$ | O O O O X . .
$$ | . 1 . O X . .
$$ ---------------
- Click Here To Show Diagram Code
[go]$$B Black kills White
$$ | . . . . . . .
$$ | X X X X X . .
$$ | O O O O X . .
$$ | . 1 . O X . .
$$ ---------------[/go]
Black
kills the white stones, because their eyespace is reduced to 1 eye.
Black

does not
capture the white stones, because they still have two liberties. In fact ...
$$B From kill to capture - 1
$$ | . . . . . . .
$$ | X X X X X . .
$$ | O O O O X . .
$$ | 2 X 1 O X . .
$$ ---------------
- Click Here To Show Diagram Code
[go]$$B From kill to capture - 1
$$ | . . . . . . .
$$ | X X X X X . .
$$ | O O O O X . .
$$ | 2 X 1 O X . .
$$ ---------------[/go]
If next Black decides to capture the white stones, reducing their liberties to 1, the maneuver needs to go in 3 steps.
After

White can capture the two stones at

.
$$B From kill to capture - 2
$$ | . . . . . . .
$$ | X X X X X . .
$$ | O O O O X . .
$$ | O 3 4 O X . .
$$ ---------------
- Click Here To Show Diagram Code
[go]$$B From kill to capture - 2
$$ | . . . . . . .
$$ | X X X X X . .
$$ | O O O O X . .
$$ | O 3 4 O X . .
$$ ---------------[/go]
In the resulting position,

again goes for capture, but again White can postpone being captured, by capturing herself at
$$B From kill to capture - 3
$$ | . . . . . . .
$$ | X X X X X . .
$$ | O O O O X . .
$$ | O 5 O O X . .
$$ ---------------
- Click Here To Show Diagram Code
[go]$$B From kill to capture - 3
$$ | . . . . . . .
$$ | X X X X X . .
$$ | O O O O X . .
$$ | O 5 O O X . .
$$ ---------------[/go]
Finally White has only one liberty left and Black :b5:captures all 7 stones, as in the very first diagram.
The whole sequence of mutual captures goes to show that Black has originally
killed White, in the second diagram.
Now what did I mean with worry free?
$$B Black kills White
$$ | . . . . . . .
$$ | . O O O O O .
$$ | X X X X X O .
$$ | O O O O X . .
$$ | . 1 . O X . .
$$ ---------------
- Click Here To Show Diagram Code
[go]$$B Black kills White
$$ | . . . . . . .
$$ | . O O O O O .
$$ | X X X X X O .
$$ | O O O O X . .
$$ | . 1 . O X . .
$$ ---------------[/go]
Just like in diagram 2, Black

killes White by reducing the eyespace to 1 eye. However, Black is not worry free: the black chain has 3 liberties, against White's 2 inside. Black is ahead in the capturing race but needs to be mindful of his small advantage.
$$B Counting liberties
$$ | . . . . . . .
$$ | . O O O O O .
$$ | X X X X X O .
$$ | O O O O X 2 .
$$ | . 1 3 O X . .
$$ ---------------
- Click Here To Show Diagram Code
[go]$$B Counting liberties
$$ | . . . . . . .
$$ | . O O O O O .
$$ | X X X X X O .
$$ | O O O O X 2 .
$$ | . 1 3 O X . .
$$ ---------------[/go]
When White

reduces Black to 2 liberties, it's not sufficient for Black to have killed the white stones in the corner. He must set out to effectively capture them, starting with

as in the above sequence of captures.
If there's anything unclear about the above, ask freely.