Can you please explain the difference between FARTHER and FURTHER? Please provide examples too! thanks!

Farther is specifically limited to physical distances - though, of course, we all use it incorrectly all the time. Further is used either for abstract distance or for some non-physical distance discussion. Just remember that physical distance = far(ther). Everything else is further.

I ran farther than you did yesterday.

I hope that airline prices drop further before I have to buy my ticket.
I need to look further into the options for our vacation.