The HSSP stands for Homology-derived Secondary Structure of Proteins. It was designed by Chris Sander and Reinhard Schneider. They wanted to use HSSP to aid with the prediction of the secondary structure of proteins. Hence the name: Homology derived Secondary Structure of Proteins.
In practice it was Burkhard Rost who, in his PHD software, used MSAs (multiple sequence alignments) as input to his neural networks for secondary structure prediction, and thereby gave HSSP an enormous popularity boost. If you read the older Rost and Sander articles on this topic, you should especially look at the acknowledgments to see who made this connection (Improved prediction of protein secondary structure by use of sequence profiles and neural networks B Rost, C Sander PNAS 1993, 90:7558-7562)
Since 2000 the HSSP is maintained by Elmar Krieger who, starting in 2004, got help from Maarten Hekkelman. Today, Maarten makes sure that the HSSP database is always up-to-date.
Lately, Maarten makes sure that you get every week full access to the latest HSSP files.
The original HSSP article and the first article about HSSP file distribution are available. Especially the NAR article about distribution is no longer up-to-date; it is merely listed here for completeness.