The Student Edition 12.0 is designed for 64 bit Operating System (windows specifically)
64-bit refers to the size of the address space. When you compile a 32-bit program, the code is turned into assembly language and each instruction has an address that is 32-bits long in memory. Conversely a 64-bit program uses a 64-bit address. The real advantage is that any given program can access a lot more memory in a 64-bit system.
Also, 64-bit processors are instruction set compatible with 32-bit (on the same instruction set). That is, a 64-bit processor should have no issue running a 32-bit program. In the case of IA-32 and x86_64, this is handled by a library in the OS that truncates the memory addresses in a predictable way.
The reason you can’t run 64-bit program on a 32-bit OS (even on 64-bit hardware) is because the OS is only concerned with half the memory address, and it gets instructions that don’t make sense to it.
