The Valar were the fourteen (fifteen including Melkor) Ainur who entered Arda after its creation to give order to the world and combat the evils of Melkor. They helped to begin the shaping of Arda through the music of Ilúvatar. Each of the Ainur added his or her own part to the music creating the world incarnate. All except Melkor. His vision of what Arda should have been was different than Eru's. This led to the casting out of Melkor and his great rebellion that caused so many of the ills of the world of Arda. The Valar originally dwelt on the hidden Isle of Almaren, but after its destruction, long before the Awakening of the Elves, they moved to Aman and founded Valinor.
It was originally Melkor's intention to rule Arda from himself, but Manwë called other spirits to help him confront Melkor. Among these were the other Valar and the Maiar. Melkor withdrew from Arda, and the others continued their creation of the World. But Melkor saw this, and returned to fight for control of Arda. The Valar have no fixed shape, but often take the shapes of Men and Elves, or anything they want, or they can remain invisible. They are not gods, though Men often mistake them as such. They are actually emissaries or regents of Ilúvatar, or Eru, the monotheistic God of the world, who rarely directly intervenes in the world's course of events.