Farther refers to distance.
Example: At baseball camp, Jack learned that with the correct stance and technique, he could throw the ball farther this year than he could last year.
Further indicates “additional degree, time, or quantity.” It can also be used as a verb.
Example: I enjoyed the book to a certain degree, but I felt that the author should have provided further details about the characters.
Example: Kim furthered her education by taking summer classes.