This is Dali’s surrealist interpretation of the Greek myth of Narcissus. Narcissus was a great beauty who broke many hearts but fell in love with his own beautiful reflection in the water and drowned. The gods immortalised him as the narcissus (daffodil) flower which appears in the painting.
Dali took this particular painting to a meeting he had with Sigmund Freud in London in 1938. Freud was impressed but the picture and by Dali.
The original oil painting of this can be seen in the Tate modern in London.