People write down things like weather measurements such as temperature, athletic times in Olympic races, and election results. To write something down is to record it. ("Record" here is a verb with the accent on the second syllable). The written account is called a "record" (noun, accent on the first syllable).
If we look at, say, the temperature someplace, there will be some number in the record that is highest. That extreme value is often called "the record." If today's temperature is higher than any temperature previously recorded, we say it "broke the record." If an athlete runs 100 meters faster than any time ever previously recorded, the athlete "broke the record" or "set a new record."
Election turnout is one of these numbers we track and record. "Turnout was projected to be a record low" means "turnout was projected to be the lowest number ever recorded, lower than the previous record."