The game is based in Dunwall, where a corrupt government has been set up after the murder of the High Empress, a murder you've been framed for. After you (Corvo) escape from prison you team up with the Loyalists, carrying out a series of assassinations and missions in order to clear your name and return the government to normalcy.
In order to aid you on your quest, a man named the Outsider gives you the ability to have supernatural powers. The first power you get, for free, is called Blink. It allows you to teleport over a short distance without being seen. There are more powers you can obtain, but first you must collect Runes. Runes are scattered throughout the world and allow you to upgrade and obtain new powers, including Possession and Time Warping.
Here's a picture of a Rune
The game is extremely good, but it also requires patience. Even if you want to kill everyone, you still have to be smart about it. I've met the game over screen many times for not thinking things through completely, or for failing to see a guard. The game involves a lot of trial and error, so it is wise to save often.
The missions themselves are quite extensive, usually involving multiple objectives. On your missions you can also roam around a bit to find Runes and Bone Charms. Bone Charms are attributes you can add to your character to gain more of an advantage, but you can only have three equipped at a time.
Honestly, I went into playing this game with no predisposition. I didn't expect it to be as good as it is. The game is a much need break from all the typical games. I can say that this is the best game I've played all year, and it deserves to be played.