People were having this same debate just a few years ago with desktop processors. In a nutshell, certain application that require processor-intensive tasks like encryption/decryption and encoding/decoding of audio and video, can benefit from 64-bit processors, if compiled for it.
Larger files can also be handled much more easily. And, when the time comes to add RAM to iPhones, 64-bit processors can address more than 4GB of RAM, BUT, it's not true that you NEED more than 4GB before you see any benefits from 64-bit architectures.
I can say that VPN software, for one, will take advantage of 64-bit hardware... in fact, it HAS to. The 32-bit versions of OpenVPN and Juniper SSL VPN stopped working on the 5s, and the apps had/has to be updated to work.