The math is something like this:
Old school computers were capable of running 8-bits of data at a time in the CPU registers. This allowed a total addressable memory of (binary numerical system) 2^ (bits) 8 = 256 bytes.
Then 16-bit CPUs, starting with the 386, were designed capable of running 16-bits of data in its registers and was able to address 2^16 = 65,536 bytes memory. This was back in the MS-DOS and early Windows 3.1 days. By the time Windows 3.1 was released people were experiencing lag and very poor performance using this OS due to the lack of memory addressing required to render the images displayed on screen.
Windows 95 then submerged with the Intel Pentium CPU capable of addressing 2^32 = 4,294,967,296 bytes or roughly 4GB of addressable memory and a huge difference was noticed that changed the computer industry. This obviously included OSs such as Windows 95, 98, ME and XP (32-bit).
The new evolution of the 64-bit processors brings the capability of processing 64-bits of data in its registers allowing it to address memory up to 2^64 = 18,446,744,073,709,551,616 bytes or 18.4EB (ExaBytes) of addressable memory. This number is hard to fathom as it would take 18 quadrillion (18,014 trillion) 1GB sticks of RAM to fully take advantage of this capacity compared to the 4GB max earlier, and still widely used, 32-bit processors can handle.
This means that the difference in 64-bit processors compared to 32-bit processors is the same as what people experienced when the 32-bit processor, or Pentium, was invented and the transition from MS-DOS (16-bit) to Windows 95 (32-bit) took place. We saw a large difference although few truly understood what had taken place to allow such a transition. We are in the same boat today; it will take some time for us to fully utilize the processing power of the 64-bit processor and come to use an OS that will make such a difference as Windows 95 did back in the Windows 3.1 and DOS days. Hopefully that clears it up. BTW, I didn't read all the posts so don't complain if someone already mentioned this. Just thought I'd throw in my two cents