I received 9 responses to the photograph is the previous post, 7 of which were dead on. I suspect that the seven all had some fire service or first responder background. The other two responses were really close, figuring that the image was that of a trampoline.
The photo was that of a life net, one that hangs on the wall of a fire station. From some of your comments, it appears that firehouse walls seem to be a common location to find them. From condition of the few that I have seen, they must not have been used a whole lot. This one is in great shape, other than the leather straps beginning to show signs of rot.
I don't know anyone that has ever used one, even in drill. To me the concept seems high risk, especially for civilians. Hitting the center appears to be critical, as does landing properly. I've been told that three or four story jumps were possible. No thanks, I'll take the stairs!
I did ask the owners of this life net if they would demonstrate it for me, I had no takers on that one. I did manage to scrounge up the following video, It appears to have shot in the '60s and features the Detroit F.D.
I noticed that the life net that appeared in the video had metal springs where the canvas connected to the frame. It appears that the springs would provide a little more "give" than the leather straps and might be a bit more durable as well.
If you know of any agency that still uses one of these things, let me know - it might be worth a follow up.
Thanks for the comments and of course, thanks for reading,