The Wikipedia article on 'Presidents of Germany (1919-1945)' explains the Presidential election system.
The purpose of the second round seems to be that candidates with no chance would (hopefully) withdraw and that similar groups could combine to support the same candidate.
I think that the Germans adopted the second ballot system, as it existed in the French Third Republic. The second ballot system was discussed, in a book published in 1911 (now available through the Project Gutenberg website), Proportional Representation by John H. Humphreys.
