Valar
The Valar, the Powers of the World, were the great spirits who shaped and governed Arda, the world, under the authority of Eru, the One. Before the world was made, Ilúvatar brought forth the Ainur, the Holy Ones, offspring of his thought, and taught them the great Music from whose themes the world was first conceived. Those mightiest of the Ainur who descended into the world to order and tend it became the Valar, often called the Gods by Men, though they were not such, being the servants and stewards of the One.
There were originally fifteen of the Valar, but one fell into evil -- Melkor, the mightiest of all, who turned to malice and was thereafter named Morgoth, the first Dark Lord. The remaining fourteen, seven lords and seven queens (the Valier), labored to heal the world's hurts and to defend the Children of Ilúvatar -- the Elves and Men -- against his corruption.
The Powers
Chief among the Valar was Manwë, lord of the airs and winds, dearest to Ilúvatar and king of Arda, who dwelt with his spouse Varda (Elbereth), kindler of the stars, upon the holy mountain of Taniquetil. Among the others were Ulmo, lord of the waters; Aulë the Smith, maker of the mountains and craftsman who fashioned the Dwarves; Yavanna, giver of fruits and lover of all growing things; Mandos, keeper of the Houses of the Dead and speaker of dooms; and Oromë the hunter, among others.
The Valar made their dwelling in Valinor, the Blessed Realm in the uttermost West, beyond the Great Sea, where they raised the Two Trees that lit the world before the Sun and Moon.
History
The Valar warred long against Morgoth in the Elder Days, and at the end of the First Age they overthrew him utterly and cast him into the Void. Thereafter they withdrew somewhat from the direct governance of Middle-earth. Yet they did not wholly abandon it: when Sauron, Morgoth's chief servant, rose anew, it was the Valar who sent the Istari -- the wizards, lesser spirits called Maiar -- into Middle-earth to aid the free peoples against him.
Significance
The Valar are the architects and guardians of the world, the highest powers beneath Ilúvatar himself. Their care, their restraint, and their distant aid through the Istari shape the whole history of Middle-earth, and the fall of one of their own number in Melkor is the wellspring from which all the evil of the ages flows.