The moths don't but the caterpillars that become the moths do the eating. They can digest the fibres in the cloths more efficiently than we could if we ate clothes. Clothes have a calorific value like anything else.
Clothes moths are attracted to fibrous natural fabrics like wool, esp. if they are soiled w/ food or perspiration which add extra protein. The larva can do a lot of damage. Keep nice woolen clothes clean and in garment bags.
Ah because we dont have enzyme we require to convert fibre to energy but are you saying that the moth does? good point about perspiration, we loose some sugars and electrolytes through sweat, so i guess they would prefer used clothes opposed to fresh