killing
There are two ideas that are important to distinguish for a beginner:
- taking the opponent's stones;
- killing a group belonging to the opponent.
In the first case the stones are actually taken off the board. In the second case the group is put in a position where it has no long-term future (in particular cannot make two eyes). It may possibly survive, in a few ways: ko, attacking the outside groups successfully, connecting unexpectedly.
Unfortunately and somewhat confusingly, 'capture' may be used in both senses.