Iguanas are reptiles and nearly all reptiles lay eggs. There are some reptiles that do not lay eggs, but they are very rare. Female iguanas usually lay a clutch of eggs every year once they're mature. If there is no male iguana, she will still lay eggs, but they won't be fertile. If iguanas mate, several weeks after mating, the female green iguana digs a nest and lays about 20 to 60 eggs. The eggs are left in the nest and hatch about 3 to 4 months later.
For more on iguana reproduction, check out this website: iguana-reproduction
For more on the iguana in general, see this Wikipedia article: iguana
For more on reptiles, see this Wikipedia article:reptile