The key word is by which means that to swim each 50-meter section of the race takes longer than the previous 50-meter section by 12 seconds. i.e. Section 1 (60secs.), Sec. 2 (72 secs), Sec. 3 ( 84secs.)...........Then he slows down by 12 seconds for each of the next 50 meters of a race.
Without the word by, the sentence would read, "Then he slows down 12 seconds for each of the next 50 meters of a race." which means that the slow-down period is the same for all the sections after the initial one.
Another example; "At the auction, the bidding price was raised by $10 each time." ( e.g. If the initial bid was $100, the next consecutive bids would be $110, $120, $130, $140.......)