The narrator points us to The Hobbit (which is supposed to be part of the "Red Book of Westmarch," written by famous Hobbit Bilbo Baggins) for more information.
The Hobbit by J.R.R. Tolkien is the 1937 precursor to The Lord of the Rings. This is a delightful prequel.)
The narrator continues: Hobbits are small people who "love peace and quiet and good tilled earth" (prologue.1.3). Don't we all?
They are skillful with their fingers, like bright colors, and enjoy living in peace. They also have really hairy feet with thick, leathery soles, so they don't have to wear shoes. Kind of gross.
By the time of the events in The Fellowship of the Ring, Hobbits have lost track of where they came from originally, as a people.
They're clearly closer to humankind than they are to Elves or Dwarves, though.
There are three kinds of Hobbits: the Harfoots, who live near the mountains and enjoy holes in the ground and the company of Dwarves; the Stoors, who like riverbanks and are "less shy of Men" (prologue.1.10); and the Fallohides, who are a bit taller than other Hobbits and hang out with Elves.
The Harfoots are the most common kind of Hobbit: they still live underground, and they like to settle in one place.
Hobbits count time starting with the year they crossed the River Brandywine into the Shire.
The Shire is a large square of land which is also the center of Hobbit life and culture in the Third Age (Age the events of The Lord of the Rings happen).
Relative to the other lands of Lord of the Rings (Gondor, Rohan, Mordor, etc.), the Shire is in the northwest, in the region of Eriador.
The Shire has been peaceful for centuries; in fact, the narrator assures us that "At no time had Hobbits of any kind been warlike, and they had never fought among themselves" (prologue.1.17).
Underneath the Shire are a ton of Hobbit holes (called smials), many of which house huge Hobbit families (like the Tooks or the Brandybucks).