"개가 섬까지 수영합니다."
Translation:The dog swims to the island.
-까지 can be used in sentences to have the meaning of “to/until a place/time.”
-(으)로 means many different things (check the link) but in the cases it translates to "to", I believe it's used to "indicate the direction that something is happening in". So like, "towards" basically.
Well, if I saw a dog swimming to an island, I would be pointing it out as that is not common. Look! The dog is swimming to the island. Now this seems to be something the dog does on a regular basis which is all the more reason for it to be not just any dog. If he does it on a regular basis, then there must be a reason and now the island is probably not just any island either.
In verbs of motion, "towards" implies a direction, but not necessarily a destination, while "to" typically implies destination. For example, if you swim north, you are swimming towards (or toward is slightly more common in American English methinks) the north pole, but you are not swimming to the north pole unless you actually will actually arrive at the north pole.