In the case that wasn't an exaggeration, the quest of the dwarves was to reclaim the Lonely Mountain (their former home) from the dragon Smaug. They enlisted the help of Gandalf and, because 13 was presumably an unlucky number, enlisted a 14th member, which Gandalf convinced them should be Bilbo as he could "burgle" for them. Gandalf, though, almost always ends up being elsewhere (presumably dealing with the Necromancer a.k.a. Sauron in the south end of Mirkwood, which seems to be more Gandalf's 'quest' throughout this time). There's a little more once they complete their quest, but that's the meat of the goal for the main characters (well, and that Bilbo secretly wants to go on an adventure).
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