Gandalf comes to the home of Bilbo Baggins to ask him to go on an adventure. His ultimate goal is to have Bilbo join the dwarves on their journey to Lonely Mountain, where they will have to defeat Smaug the dragon. Contrary to what Bilbo believes, Gandalf believes that the hobbit has both the mettle and courage to make the trip, and characteristics that will make him useful along the way.
The invitation to adventure is initially flatly refused by the hobbit, who considers adventure to be something that "makes you late for dinner." He makes it abundantly clear that hobbits live a simple life and "have no use for adventures."
When Gandalf mentions his former association with Bilbo's mother, Belladonna Took, Bilbo suddenly realizes to whom he is speaking and remembers the many wonders of which Gandalf is capable. It seems unlikely, initially, that Gandalf is going to get what he came for, because Bilbo is quite adamant that he does not want anything to do with an adventure, although he does invite Gandalf to tea the next day.
It could also be argued that Gandalf comes to the home of Bilbo Baggins to bring upheaval and surprises into Bilbo's life, which begins to happen when dwarves, instead of the wizard, begin arriving for tea the next day. Before long, Bilbo's home seems to be overflowing with dwarves, and by the time Gandalf arrives, the wizard has already succeeded in making Bilbo feel completely overwhelmed, whether or not this was his intention.