I'm not sure I can think of a cuter common name for a plant than 'petticoat daffodil.' I mean, really. The botanical name, bulbocodium, means 'woolly bulb' which is somewhat (conversely) less cuddly-sounding. Paghat's Garden quotes a great line of Mother Goose that refers to this plant:
Daffy-down dilly has come to town
In a yellow petticoat and a green gown.
Of course, this specimen is a white cultivar, which I think is somewhat less striking. The fine, threadlike leaves and the small white blossoms get lost in this planting, near the USBG. I much prefer the straight species and its yellow flowers.
I blogged about daffodils and their many classes on NYPAOS. As you can see, N. bulbocodium has a greatly enlarged cup and small, flared perianth. Like many other bulbs, this species is native to the Mediterranean, specifically Spain and Portugal.