The basic rules of go state that when a group's last liberty is removed, the group is captured. It follows that if a group has at least two liberties which cannot be removed, the group cannot be killed and is alive. All subtleties aside, such an unremovable liberty is what we call an eye.
Look at the circled points. A white stone placed on either of them would be disconnected from the other white stones and would have no liberties. Both black chains would still have the other circled point as a liberty. Such a move by White would thus be illegal. Neither of the two circled points can be occupied by White without the other. In conclusion, the circled points are two unremovable liberties of the black group, or two eyes, and it is impossible to remove the black group from the board (without Black stupidly filling one eye).
- Check out the Smallest Group with Two Eyes.
- There is a formal definition of two-eye-formation.
- Note that sometimes a group may have a single eye with more than one point in it, but that does not neccessarily make the group alive: separate eyes are required.
- Often, a liberty that appears to be an eye may actually be removable by the capture of a chain of stones; see False Eye.
- Read more in Eyes Collection and Life and death