Milk is converted into curd or yogurt by the process of fermentation. Milk consists of globular proteins called casein. The curd forms because of the chemical reaction between the lactic acid bacteria and casein. During fermentation, the bacteria use enzymes to produce energy (ATP) from lactose. The byproduct of ATP production is lactic acid. Lactic acid acts on the globular proteins present in the milk and denatures them. This denaturation destroys the tertiary and quaternary structures of proteins and the globular proteins are converted into fibrous proteins thus giving a thick texture to the milk due to coagulation of the proteins.
