Tennessee Williams includes the iguana as a live animal and makes it a symbol that stands for the human condition, especially in reference to specific characters who are limited or restrained in various ways.
The animal is a harmless creature that people have tied up to consume in the future. While all the characters must deal with particular limitations, Larry Shannon is especially held back by emotional problems, including loss of faith and the long-term effects of alcoholism. For much of the play, he seems to be at the mercy of those forces, much like the iguana is helpless to overcome or escape from its restraints. At one point, Maxine even ties him up to prevent him from destructive behavior. It seems he has not much farther to fall, and he strikes up an unlikely friendship with Hannah Jelkes, who is a companion to her grandfather, Jonathan “Nonno” Coffin.
The positions of Hannah and Nonno also show severe restraints. Nonno, once a famous poet, is now at the end of his career and—as shown later in the play—at the end of his life. Hannah has virtually no life of her own, as she dedicates herself to caring for and traveling with Nonno. Conversations with Hannah, who is presented much as a secular nun, inspire Shannon to reevaluate his options.
Ultimately, he unties the iguana and, in freeing the animal, also frees himself. Rather than trying to evade his personal demons, he achieves release by confronting them. Once he has announced his act of freeing the animal, it is revealed that Nonno has died. That event releases him from the frustrations caused by his declining powers but frees Hannah to pursue an independent life.