Quendi is the name that the Elves (the Firstborn Children of Ilúvatar) gave to themselves, in J. R. R. Tolkien's fantasy world Arda. The name means, those with voices; when they first came into being, they found nothing else in the world that spoke or sang.
The Quendi appeared at Cuiviénen in Middle-Earth, at first unnoticed by the Valar living in Valinor (but probably not by Melkor, who lived in Utumno in the Northern part of Middle-Earth). They appeared before the Sun and Moon were in the sky; the first sight they saw were the stars, which were created by the Valië Varda; Varda Elentári thus was most beloved of the Valar among the elves.
The Elves were sundered into several different groups: when the Valar (Oromë in particular) invited the Elves to join them in Valinor, some went (afterwards known as the Eldar) and some didn't (the Avari). Those that went, and saw the light of the Two Trees of Valinor before they were destroyed by Melkor, are called Calaquendi: "Elves of the Light". Those that started the journey but halted, or turned back, are called the Úmanyar. The Úmanyar (except for Elwë) and the Avari collectively are called Moriquendi: "Elves of the Darkness", the Elves who never saw the light of the shining, glittering Trees Telperion and Laurelin (the sources, respectively, of the Moon and the Sun later). (Ingwë, Finwë, and Elwë are all Calaquendi; they were brought to Valinor by Oromë even before the Eldar-Avari split.)