furthest
At the greatest distance or most advanced point from something.
Furthest means the greatest distance away from a starting point. When you throw a ball as far as you possibly can, that's the furthest you can throw it. If your friend lives on the opposite side of town from your house, she might live the furthest away of all your friends.
The word can describe physical distance, like the furthest planet from the sun (Neptune), or it can describe progress toward a goal. If three students are reading the same book, the one who has read the most pages has gotten the furthest in the story. When a runner is furthest from the finish line, they have the longest distance left to cover.
You might also hear people use farthest to mean the same thing. Both words are correct, though farthest typically refers to physical distance while furthest can describe abstract ideas too. A scientist might say her research has gone the furthest toward solving a problem, meaning she has made the most progress.