Zeus and were thought of as residing in particular 'natural' habitats such as rivers, mountains, trees and the ocean.
Traditionally they were imagined as young and beautiful women, and were frequently associated with individual gods such as Pan, Hermes, Apollo, Dionysus and Artemis. They also accompanied Satyrs and the Sileni. (Later they became more 'folksy' and took on the general nature of rather 'twee' fairies.)
According to where they lived, they were divided into Orders' such as Dryads, Hamadryads, Meliae, Oreads, Naiads, Nereids, Oceanids and the like (see these names). Their general name, which is related to English 'nubile' and 'nuptial', is simply the word (nymphe) for 'bride', 'young marriageable woman'. This may possibly have originated from a verb nybo, 'to cover', 'veil'.
The diminutive word 'nymphet' is not of classical origin - it was devised as recently as 1955 by the author Vladimir Nabokov for his novel Lolita to apply to sexually attractive young girls who 'to certain bewitched travellers . . . reveal their true nature which is not human, but nymphic (that is, demoniac)'.