These two English words are very similar; keep reading for further information.
Farther means "more far/distant" in physical space.
Farthest means "the most far/distant."
Further means "more far/distant" figuratively or non-physically, and can also mean "more/additional":
Further is also a verb: "to advance":
Furthest means "the most far/distant" figuratively.
The Bottom Line
Many English speakers use both farther and further to mean "more far" in space, but only further can be used for non-physical distance and to mean simply "more." If you are talking about actual distance, you can usually use either word without raising any eyebrows, but keep further in mind for all of your English furthering efforts.