President Kennedy suffered from extraordinarily poor health throughout his life and was read the last rites by a Catholic priest twice before he had reached the age of 30. Among his many afflictions was Addison's disease, a potentially life-threatening condition. Later in life, he suffered from chronic back pain. The combination of illness and pain required significant doses of medication. In this telephone call, President Kennedy asks White House physician Admiral George Burkley to "send up a little extra medication."
See also Marc Selverstone's op-ed in the Boston Globe on March 9, 2006, available here.