It sounds exciting, but the real benefits are a little harder to understand. First, and not so importantly, 64-bit chips can address more memory than 32-bit chips. This is important in a desktop computer, where a 32-bit chip can only handle around 3.5GB of RAM, but in a smartphone where 1GB or 2GB of RAM is all thats required, this is only something that will become important in the future.
More importantly, moving to 64-bit means that the Apple can use a newer ARM architecture. The ARMv8 core now has double the number of general-purpose registers, compared to the ARMv7 used in the A6, with 31 64-bit wide registers.