This is a concept in psychoanalysis that some people find quite difficult to understand. It deserves a longer treatment than I will give it here, consider this a taster.
To understand potential space it may be best to think in the terms of semiotics. Imagine a triangle with the following labels placed on the bottom left, bottom right, and top: signified/world on the left, interpreter/person on the right, and sign on the top. By definition, signs are arbitrary, that is, there is never a one to one correspondence between the sign and what it stands for (i.e., the signified). The sign, however, does represent the relationship between the interpreter and the world.
Potential space refers to the space between the sign and the signified that allows for the flexible narrative reconstruction of experience. In a transference relationship in psychoanalysis, the analysand relates to the analyst as if he or she is someone else. Consider a father transference. The analyst has become a sign standing for the father, but later in the session the analyst may stand for other people as well. A person at a neurotic or mature level of ego functioning is able to play with the arbitrariness of the sign in this way. To the neurotic, the analyst is just like his father, but also like his mother, and his therapist as well.
At a borderline or psychotic level of ego functioning, the patient is often convinced that his or her interpretation of events IS an accurate depiction of reality. Such an experience is one of certainty and inflexibility. The space between the sign and the signified has disappeared, or in other words, the potential space has collapsed.
Later, I will elaborate on different ways that potential space can be modified. For now, I point you toward Dr. David Ogden's book Matrix of the Mind for a far more detailed explication of these ideas.