Origin: Old English
Meaning: derived from Old English dægeseage meaning "day's eye", getting its name because it opens up when the sun rises and closes its petals when it goes down.
Daisy has also been used as a nickname for Margaret, likely because its French form Marguerite, is also the name for the oxeye daisy.
In the language of flowers, daisies symbolize purity, innocence, simplicity, that the sender can keep a secret, and true love because apparently a daisy flower is made up of two different flowers. Apparently, daisies are also known as thunder flowers because they peak during thunderstorms and represent protection from lightning.
In Romany mythology, Vertumnus (the god of gardens and trees) saw a lovely wood nymph named Belides and wanted her, however she didn't want him at all. She ran away from his advances but when it seemed like he was about to catch up to her she turned herself into a daisy (the genus of daisy is named bellis after her). This reminds me a little of the myth of Apollo and Daphne from Greek mythology.