Frodo Baggins’s home village in Tolkien’s Middle-earth is Hobbiton.
Hobbiton is a settlement in the Shire, the homeland of the hobbits. It is built among the green hills of the Westfarthing and includes the distinctive round-doored homes associated with hobbit life. Bilbo Baggins and Frodo Baggins both live there at important points in the narrative.
Bilbo’s birthday party takes place near Hobbiton at the beginning of The Fellowship of the Ring. After Bilbo leaves, Frodo inherits Bag End, the comfortable smial that becomes his home. Gandalf later reveals that Bilbo’s ring is the One Ring, beginning the chain of events that sends Frodo away from the Shire.
Hobbiton is sometimes confused with the entire Shire, but they are not identical. The Shire is a larger region containing many settlements, including Hobbiton, Bywater, and Michel Delving. Hobbiton is the specific village named in this question.