You are correct they clamp onto the fork. They allow the use of a caliper brake that does not need a pivot bolt mounted into the frame. They gain leverage by clamping to front fork or the rear stays. Some of the lightweights from the 1930s-40s use these because their fork crowns and chain stays were drilled as if the bike would only have a coaster brake. You could then (or the factory could) add these clamp-on brakes to get calipers onto your bike without needing appropriate frame holes.
The most common caliper of this type found today is the "Philco" add-on type brake. I owned a pre-war Westfield lightweight with one on the front. The fork was drilled from the bottom as one would drill a balloon tire bike, so the clamp-on brake is used to get around the fact that there's no place for a brake caliper pivot bolt. It's a different maker, but same principle.
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That's not to necessarily say your brake has to be pre-war - they made these parts for many years. But it's a relic from a time when you might throw one of these heavy brakes onto a utility or transport bike in order to add braking, but where you don't have the frame holes to do it.