For plant based fibers, it’s the cellulose. When cellulose is both wet and heated, it’s fibers weaken, and become pliable. When they dry back out, those fibers are molded into whatever shape they were in; and they regain their strength.

This is where wrinkles come from. the iron applies both heat and moisture through the steam to momentarily soften the fibers, and the flat plate and weight of the iron creates a smooth, flat shape as the heat dries them out.