Jerry never finishes telling his story of the zoo to Peter. However, we do know that he needs, somehow, to make human contact of some sort. The fact that he went to the zoo relates to the fact that his epiphany as a result of his confrontation with his landlady's dog. Jerry believes that relationships must be achieved gradually; that we shield ourselves and seal ourselves off from each other, and communication is something that must be re-learned, step by step.
This is a recurring theme in Albee's work. Characters find themselves isolated, somehow unable to make meaningful with others. His plays deal with their constant efforts to break through and rediscover love, friensdhip, or even - through others - a sense of themselves.