Upon the defeat of Melkor/Morgoth, the Vaiar wished to grant their warriors great rewards at the End of the First Age. The Elves were allowed, if they wished, to return back to the Undying Lands, along with their immortality. For Men, the Vaiar created a Great Island west of Middle Earth, and allowed Men to settle and rule it, as long they made one promise: that they would never sail so far west that they could not see Numenor, for Men were never to come to the Undying Lands. The Men of Numenor at this time agreed, for they did not see immortality as a thing not be wished for -- an idea that would change over time.
Numenor, a star-shaped island with its holiest mountain at its center, soon became the base of the greatest Kingdom ever seen until that time. Numenor soon became the land with the greatest blacksmiths (called "Western" Made, often used to great effect against evil), the greatest horses, the greatest technology, the greatest warriors, and the greatest leaders. It is no surprise that once Numenor, the island, was made as great as it could be, Numenor expanded into Middle Earth into the lands of Arnor and Gondor. Making quick friends with the various Elf Kingdoms, peace and prosperity was ensured. But while they were honorable rulers at first, they soon ruled Middle Earth with more of a tyrant's hand.
The Numenorians, after nearly three thousands years of prosperity, became divided into two philosophies: one, the Faithful, wanted to continue the old ways, respect the Gods and be friends with the Elves. These would become the Dunedain, for it was not the who would cause the end. The other desired immortality, great power, and more land. These men, called the King's Men, would eventually become the Black Numenorians. The leader of this group, Ar-Pharazon, would eventually marry the King's daughter and usurp the throne. Defeating Sauron in Mordor, Sauron became his adviser... and soon, Ar-Pharazon converted to Morgoth, and sailed against the Undying Lands. The Gods repaid this defiant act by sinking the Island of Numenor, forcing the survivors to flee to Middle Earth. Thus, the Second Age ended. The Third would start with the founding of Gondor and Arnor... and Sauron leading his legions into battle once more.
Trivia: The Event of Numenor's downfall is called in Quenya (High Elvish) Atalante, a.k.a. Downfallen. Just in case you couldn't guess what Numenor was supposed to be referencing.