John Thornton’s friends can’t save him, so Buck jumps in.
When John Thornton falls into the river, he is gone before his friends even reach him. The river is moving too fast, and Buck jumps in instantly.
Buck had sprung in on the instant; and at the end of three hundred yards, amid a mad swirl of water, he overhauled Thornton. When he felt him grasp his tail, Buck headed for the bank, swimming with all his splendid strength. (ch 6)
Buck swims with all his strength, which is formidable, but he can’t get Thornton out. The others try to help, throwing a rope to Buck like a boat. After a few false starts, Buck is able to get Thornton out of the river. Buck is half-drowned and has broken ribs. They camp there until Buck is recovered.
This incident shows Buck's devotion to John Thornton, and how well Thornton has taken care of him. Buck is well enough to save him, and not much later is well enough to win a race for him. He clearly loves John Thornton, and would do anything for him.