Dating from a point 590 years after the first rising of the Sun, the Second Age began after Morgoth was defeated in the War of Wrath and expelled from Arda. That war wrought devastation in northwestern Middle-earth; the lands of Beleriand were largely overwhelmed by the Sea, with only the realm of Lindon remaining to the west of the Blue Mountains.
The Second Age was the Age of Númenor; the great island kingdom was created and peopled by the descendants of the Edain in the first years of the Age, and as the years passed, their power grew until it surpassed that of any nation of Men, before or since. They sailed east, exploring Middle-earth and founding great cities there. Eventually, their power and pride became so great that they challenged the Valar themselves, and were destroyed.
The end of Númenor was not the end of the Second Age, though; a remnant of the Númenoreans led by Elendil escaped its wreck and founded kingdoms in Middle-earth: Arnor in the north and Gondor in the south. They formed a mighty alliance, the Last Alliance of Elves and Men, and marched on Sauron, who had grown great again, assailing the Dark Tower of Barad-dûr. With the first overthrow of Sauron by the Alliance, the Second Age came to its end.