There are two major transformations in "Leda and the Swan." First and most obviously, the Greek god Zeus transforms himself into a swan in order to have sex with Leda. Why exactly did it have to be a swan? We're not sure, but it may not be that important. In Greek and Roman literature, people and gods turned into animals all the time, and vice versa. The famous word to describe this kind of transformation is metamorphosis. The second kind of transformation is historical. The rape of Leda ends with the conception of Helen of Troy, whose abduction leads to the Trojan War and the beginning of modern civilization.
The swan symbolizes the union of higher and lower spirits: the animal and the divine. In the same way, Zeus is a symbol of both absolute truth and the meaningless cycles of nature.