Simply said, the difference between 32 bit and 64 bit architecture is, that 64 bit architecture is more capable. It allows to use more memory and offers a better performance.
In many cases, it is possible to run 32 bit software on 64 bit Windows without visible difficulties.
But in many cases, 64 bit software will not work on 32 bit Windows. It can happen that 32 bit Windows will probably even not allow you to install 64 bit software.