Farther usually refers to physical distances. Further usually refers to figurative distances.
In Middle English, the word for at a greater distance was spelled several ways, including ferder, farthere, ferdre, and forther. Farther and further emerged as the prevalent spellings by the 16th century, and for several hundred years they shared all their definitions. In modern usage, however, they have diverged in meaning (though many writers still use them interchangeably).
Examples
In these sentences, farther refers to physical distances:
Farther south, in Central Otago, there are some even harsher mountains . . . [Telegraph]
Making people park a little farther away will actually increase their exposure to danger, he added. [Red Wing Republican Eagle]
Pyzik said the testing cells would be located farther from the school than initially proposed. [Chicago Tribune]
Further refers to figurative and non-physical distances—for example:
The Dollar is extending its gains against the Euro. EUR/USD fell further to 1.3430, hitting a fresh daily low. [NASDAQ]
So the mechanism that was initially meant to be protective can become the source of further damage. [Indy Posted]
Reliable measurements of the Sun’s magnetic field are only available from 1900 onwards, so researchers used computer simulations for further back in time. [Daily Mail]
Related words
The same patterns apply to the superlatives farthest and furthest. Furthermore is an adverbial extension of further meaning in addition or moreover. The rare furthermost is sometimes used to mean farthest or furthest. In either case, the shorter word is usually better.

