"The road home"
Translation:집으로 가는 길
I think the meaning is close to this: "The road that goes home". That is why you have the 가는 (from 가다, "to go") in the sentence. Hope it helps.
I also wrote that. I think it should be correct as there is a similar sentence that uses 에 instead of (으)로. The sentence is "the road to the school is long", if I am not mistaken.