When Your Iguana Licks You, What Does It Mean?
Iguanas have a sensory organ called Jacobson's organ that allows them to detect smell, taste, and chemical signals. Iguanas learn about their environment and other lizards/people in this manner. When your iguana licks you, it's trying to figure out who you are.
Billy has also appeared in films other than Saw. Insidious, Dead Silence, and Death Sentence all featured him as an Easter egg.