Double Pipe Heat Exchangers in its simplest form is just one pipe inside another larger pipe. A hairpin heat exchanger may have only one inside pipe, or it may have multiple inside tubes. But it will always have the doubling back feature shown.
The wall of the inner pipe is the heat transfer surface.
The pipes are usually doubled back multiple times as shown in the diagram. At the left, in order to make the overall unit more compact.
One fluid flows through the inside pipe and the other flows through the annulus between the two pipes.