In Greek mythology, Narcissus was a young man of unparalleled beauty who was so entranced by his own reflection in a pond that he wasted away gazing lovingly on his own form. Where he sat on the shore, a flower of similar beauty, the Narcissus, grew, leaning lightly, as if to gaze into the water.
I always find the stories behind plant names interesting. Many of them have been lost to time, of course, but that only makes those that we do know more interesting. Then, there are those about which we speculate, but cannot be certain. "Daffodil", for instance, is thought to come from the Asphodel flower, a plant that was commonly planted near graves in Ancient Greece. The Asphodel Meadows, one section of the Underworld in Greek mythology, was thought to be an endless plain of these flowers. This was the section where the dead who had led unremarkable lives spent Eternity. The "D" in "Daffodil" most likely came from the Dutch article "de," which would have been placed before the name ("De Asphodel," more commonly pronounced "De Affodil").
The term Jonquil, which is still sometimes used for all Narcissus (especially in the Southeastern US), is somewhat more straightforeward. It comes from the Spanish diminuitive form of junco, a type of reed. In the strictest sense, the term Jonquil refers only to types of Narcissus related to the species Narcissus jonquilla, which has reed- or rush-like leaves (hence the name). The use of this name to generally refer to Narcissus is mostly fading away, and it is technically incorrect, but I am loath to try to correct a common name, especially one that is as much fun to say as is Jonquil.