Just copying and pasting from pag 1 of the rules:
"The year is 1926, and it is the height of the Roaring Twenties. Flappers dance till dawn in smoke-filled speakeasies drinking alcohol supplied by rum runners and the mob. It’s a celebration to end all celebrations in the aftermath of the War to end all Wars. Yet a dark shadow grows in the city of Arkham. Alien entities known as Ancient Ones lurk in the emptiness beyond space and time, writhing at the gates between worlds. These gates have begun to open and must be closed before the Ancient Ones make our world their ruined dominion. Only a handful of investigators stand against the Arkham Horror. Will they prevail?
In Arkham Horror, the investigators explore the city, encountering places, people, and creatures both normal and mundane. Through these adventures, the investigators hope to gain the clues and resources needed to confront and ultimately thwart the mythos threat. Early in the game, investigators seek to avoid more powerful monsters while moving around the city to gather weapons, spells, clues, and other items they will need. Later, the investigators attempt to close a few gates and seal some of the most active gates. Finally, once several gates have been sealed and the investigators have acquired valuable weapons, spells, clues, and allies, they make one last, desperate assault on the mythos, attempting to close or seal the final gates. Either they succeed and the world survives, or they fail and the Ancient One awakens for the climactic battle. Be warned: If the Ancient One awakens, the investigators are in for the fight of their lives!"
Generally speaking, all FFG rulebooks (available for free download fom this very site) begin with a short presentation of the game and the theme; so, in case of doubts, the easiest thing is downloading the rulebook, and start reading :-) Probably it's the best description you can find around.