J.R.R. Tolkien actually described himself as something of a hobbit, so let's let him define what a hobbit is in his own terms:
I am in fact a Hobbit in all but size. I like gardens, trees, and unmechanized farmlands; I smoke a pipe, and like good plain food (unrefrigerated), but detest French cooking; I like, and even dare to wear in these dull days, ornamental waistcoats. I am fond of mushrooms (out of a field); have a very simple sense of humor (which even my appreciative critics find tiresome); I go to bed late and get up late (when possible). I do not travel much. (source: The Letters of J.R.R. Tolkien. Edited by Christopher Tolkien and Humphrey Carpenter. New York: Houghton Mifflin, 1981, pg. 288-9)
No wonder Tolkien seems so fond of hobbits: he thinks he is one! And indeed, Bilbo seems to fulfill most of Tolkien's requirements: he smokes a pipe, he loves food (and is presumably a bit paunchy), he loves a nice waistcoat, and he likes a good night of sleep. He does travel a good deal – but only thanks to Gandalf – and we can't comment on the French food thing because (so far as we know) France doesn't exist in Middle-earth. But anyway, there are hobbits for you: good-natured homebodies, based on the model of the author himself.
Bilbo Baggins is not just a hobbit, he is the hobbit: the prototype of perhaps the most distinctive group of people in Tolkien's whole fictional universe. In addition to the general species traits listed above, Bilbo has a couple of other noteworthy characteristics: he loves settling in for an evening of smoke-rings with good friends. He's fond of flowers and the sound of his kettle whistling. He has a passion for maps and runes, but he also enjoys studying them in the comfort of his tidy, warm hobbit-hole. In other words, Bilbo Baggins is essentially a homebody: an ordinary guy with an orderly life.
What The Hobbit teaches us is that even someone as breathtakingly respectable and old-fashioned as Bilbo Baggins can be swept up in a wild adventure. This gives hope to the rest of us extremely average folk that, someday, Gandalf might scratch a note on our doors so that passing dwarves will bring us on treasure quests. Fingers crossed, right?
Even at the beginning of the novel, we know that Bilbo has no hope of becoming a He-Man style Hero (yes, a capital "H") wielding a broadsword and killing dragons like they're salamanders. For one thing, Gandalf tells the dwarves as much when he confesses that "in this neighbourhood [of Bag-End] heroes are scarce, or simply not to be found" (1.117). Furthermore, Bilbo just doesn't have the physique for those kinds of heroics, with his small stature and curly toe-hair.
So Bilbo is our hero (because he's the main character of the book) but he is not a hero. He has no great goals in mind as he embarks on this quest – he's mainly along for the ride, because this Gandalf fellow forces him. This makes Bilbo entirely unique in the novel: all the other characters (Thorin, Bard, even Gandalf, who's fighting for Good) have something in mind for a goal. Bilbo is a completely blank slate: he's like a baby in the wilderness.
Yet, this quest is not all about adding new elements to Bilbo's character – he's is also protected from getting carried away by his strong sense of home. Bilbo knows that what he values most is back in Bag-End. So Bilbo doesn't fall victim to the gold-sickness that almost drives Thorin crazy. And Bilbo is not proud or confrontational like Bard or the Elvenking. He's practical and loyal beyond the imagining of nearly everybody in the novel. (Think, for example, of Bilbo's decision to give the Elvenking a silver and diamond necklace in thanks for the food Bilbo stole when he was hiding in the guy's castle. Now that is being serious about honor and honesty!) In a sense, Bilbo is extraordinary. He is amazing at being ordinary.
Bilbo has spent his whole life cultivating everyday virtues like friendliness and generosity, and it is precisely these hobbit traits that make Bilbo heroic in the larger world. We totally agree with the Elvenking when he says that, even though Bilbo may not seem like much, this hobbit is "more worthy to wear the armour of elf-princes than many that have looked more comely in it" (16.40). Bilbo learns a lot as he travels with the dwarves through distant lands, but he also never changes his essential nature or forgets his roots. (For a contrasting example, check out our analysis of Thorin Oakenshield.)
One last note. While Bilbo may not be a Hero, he does have a superpower: his luck. Bilbo happens to wake up just as the crack is opening in the back of their Misty Mountain cave to let the goblins in. Bilbo happens to put his hand on the ring of invisibility in the middle of the goblin tunnels. He also walks right up to the Arkenstone of Thrain, the one thing Thorin Oakenshield wants most in the whole world, just by chance. Bilbo's luck has no explanation, but it's the one thing that gets him through all of the sticky situations that are beyond his abilities to manage.