What is the main function of the epiphyseal plates in bones?

Multiple. There are multiple functions of the epiphysis, which is basically the end of the bone. The ends of the bone have the articulate cartilage that forms the joints on the body, they contain the growth plates that allow for growth in a skeletally immature patient. They are the sites of attachment for many ligaments and tendons as well. Good question.
Bone growth. These serve as the site of bone growth/elongation. This is also sometimes called the physis.
Joint growth. The physeal plates are at the ends of your bones. This is where the longitudinal growth of bone takes place when you are still young. At skeletal maturity it closes up and no more growth occurs. "epi" means above so the "epiphysis" is the area above the physis, like the epidermis is above the dermis in the skin. The epiphsis is at the end of the bone and forms a joint with the bone next to it.
Growth in children. The epiphyseal plates are the cartilage growth areas near joints where bones grow in length. Most injuries or fractures do not affect the growth adversely, but some are serious. Xrays are needed to assess the damage.