White just played inside the black territory.
Black needs 4 stones to capture this. Thus, black may lose 3 points after capturing the one white stone. (4-1=3)
So, you keep losing points if the opponent plays inside your territories? No!
Black doesn't have to play 4 moves in order to capture one stone in the first place. Black needs to play just one move to tell white, "You can't make a life there!"
Then you gain one captured stone and lose one point by playing inside your own territory. Therefore, it's even.
You don't need to capture the invaders by completely surrounding them because you can always capture the opponent if you want. Those stones are regarded as dead stones and will be unconditionally removed at the end of the game unless they have two eyes.
You may wonder why you can tell if the white stones are dead. Let's assume white keep playing there and the result is as below.
The 4 white stones in the bottom left corner are surrounded by half while they don't have enough space to make two eyes.
If, at the beginning, black thinks his territory is strong enough and he doesn't need to respond, he could ignore the move.
For example, if white plays inside black's territory as below, he could either play somewhere else or pass a move because even if white plays one more move, white still won't able to make a life there. (In the case below, black should just pass a move because there is nowhere to gain a point. In this case, black gains one point because he didn't play inside his territory.
No matter how white plays, white stones will be removed at the end - thus regarded as dead.
The whole discussion above also means that you should try to invade if you thought the opponent should at least respond a defence move. You won't lose a point as long as the opponent respond to your move by playing inside his territory.
As always, white played a move inside the precious territory of black.
Black tried to capture them but white played better and build some territories inside black's.
In this case, black's territories got decreased by a lot - White made a territory of 9 points while black's territory decreased from 39 points to 14, which cost a game for black.
In some cases, black could lose all the territory and the entire group is dead.
At the early stage of the game, there are lot of empty spaces between stones. As the game progresses, these empty spaces are gone little by little and at the end of the game, there are "almost" no empty spaces between black and white stones. If there are really no empty spaces around your stones, you are dead. However, if there are slight spaces where the opponent can't come in - the eyes - you are alive.
For example, at the position of [Fig.2-5], assume black passes and white plays a move, and then black passes again. And then white played again. How do you see the board position?
If black dares to capture the three stones, the position will be shown as below.
At this position, white then plays at the upper right corner and can capture all the black stones.
Therefore, black should not try to capture white stones.
What if white tries to capture black stones?
Black then can capture the 4 white stones and has a clear 4-point territory.
Thus, white should not try to capture black.
This means that at the first position, both side should not try to capture the opponent.
It is regarded that both sides are alive in this case, which is called Seki.
Seki is a special case but not very rare.
On the first figure, black has 0 points and white has 5 points thus white wins by 5 points on the board (when Komi - the bonus point for white - is ignored.)