The precise meaning of the iguana in Williams's play has never been established to everyone's satisfaction. So what follows is largely speculative but nonetheless based on certain lines of critical inquiry into the play and its symbols.
On one reading, the iguana represents freedom or, rather, the lack of it. The iguana is tied up for most of the play, ready to be eaten by some boys after it has become sufficiently plump and juicy. In that sense, it has no freedom at all. However, right at the end of the play, the iguana is given its freedom after it is cut loose by the defrocked priest Shannon.
That Shannon should be the one to free the iguana is instructive. Like the iguana, he himself has been robbed of freedom in that he has found himself tied down by society's morals and restrictions, not to mention those of the Episcopal Church to which he wishes to return.
In cutting loose the iguana at the end of the play, Shannon is symbolically freeing himself from the many demons that have tormented him for so long. He can now move on with his life, establishing a professional relationship with Maxine in the management of her hotel.