Bleak Falls Barrow is the first dungeon that you come across in Skyrim. There are two main quests that require you to go to the dungeon. You have to recover the golden dragon claw for the trader in Riverwood and you have to recover the Dragonstone for the Jarl of Whiterun.
It is fairly straight forward. As usual all of the puzzles consist of finding the chain to pull on and matching the combination of images on the dragon claw to the combination on the door.