Short answers, pulled from the story.
A dryad is a tree nymph from ancient Greek mythology, with the word tracing to Drys, the Greek term for oak. Most dryads were supernaturally long-lived. The name came to be used for tree nymphs of all kinds, not only those of the oak.
A hamadryad was a type of dryad whose life was inextricably bound to a single tree, such that if the tree died, the hamadryad died with it. Other dryads were supernaturally long-lived but did not share this fatal bond with one individual tree.
The Meliae were the dryads of the ash tree. In Hesiod's Theogony, Gaia gave birth to the Meliae after being made fertile by the blood of the castrated Uranus. The Meliae sisters also tended the infant Zeus in Rhea's Cretan cave.
Greek gods and the dryads themselves punished any mortal who harmed a tree without first propitiating the tree-nymphs. The stakes were highest for hamadryads, who could not survive the destruction of their tree.
Dryads appear as full inhabitants of Narnia in C. S. Lewis's Chronicles of Narnia. In Prince Caspian, the Telmarines' felling of trees and defiling of streams forces the dryads and naiads of Old Narnia into a deep sleep, from which they awaken when Bacchus and Silenus are summoned by Aslan to fight King Miraz's army.
In his "Ode to a Nightingale," Keats addressed the nightingale as "light-winged Dryad of the trees," drawing on the figure of the Greek tree nymph.