The basic idea is that you (the radio listener) confirm by mail that you have distantly received a radio station (usually shortwave and AM) . They would send you a verified reception stamp/letter/card etc. This was really, really cool. It fell out of favor because people who thought it was really really cool were not cool at all. [Ex people like me]
The process was very simple. An number of copmpanies made these for example: For only $1.75, the Ekko Company offered an album to collector sof new verified reception stamps. The album contains pages preprinted with an outline of each of the current available and a listing of broadcast station call letters with wavelengths. The inside cover had a nice little showing the locations of these stations. Spaces were left for new stations and your own notes. It was a few years before QSL cards and it's popularity may have been what probably led to QSL cards. Note: some hams still issue QSL cards today.
Interest in the hobby became so widespread that the February 1925 issue of Radio News featured the Ekko stamps on its cover.
I think Ekko was the first to offer the binder/stamp concept but the verified reception stamp fad was so popular that it prompted other companies to issue their own stamps or seals. Of course these did not fit into the Ekko binder. You had to buy their binder. Much like the uncompatible software problems of today, consumer confusion was an immediate problem.
Incredible set of pictures here:
and KLX here: http://community-2.webtv.net/N0NNK/KLZ560/