In life and death, a group needs two eyes (two real eyes) to live. If a group is totally surrounded and has only one eye (false eyes do not count), then it would be a dead group.
This group has effectively an eye at a, because White playing at b will be self-atari. However, what is not so sure is that whether the spaces at b and c is really an eye.
The solution is to make a throw-in at . This is a tesuji, or technique, for destroying the eye on the outside.
... then turns b into a false eye. The entire group only has an eye at a, there is no eye at b. So Black is dead.
... followed by . (This sequence just proves the death - there is no need to actually play
and
, at least under some rulesets)
In the previous variation, we see that allowing White to play at will kill the group. What if Black plays at
?
This is what we call shortage of liberties. More precisely, Black suffers from a shortage of liberties. The reason is that can capture the four Black stones chain.
If White makes an atari at , then
connects and has two real eyes. Note that now White cannot play at either a or b - it is suicide.
This discussion is at a higher level than the problem and may be skipped by introductory level players on their first reading.
We now turn the problem around and ask how Black can live. There are two ways, each with their pros and cons, but usually the consensus is that one of them is better.
Now we compare both methods.
For the first way to live, Black has two points of territory at a and b. Also, White has no ko-threat.
For the second way to live, Black has three points of territory at a, b and c. However, the disadvantage is that White has one ko-threat at either b or c. On the other hand, creates a cutting-point at d, which may be used for Black's advantage in the later part of the game.
We can see that the pros of the second method significantly outweighs the cons, so the second method is usually better.