X86 is 32bit, X64 is 64bit. Your CPU is capable of handle either 32 or 64bit instruction. What determines the app version you need to install is the OS. If you are running a 64bit OS then install the x64 version of the app. If you are running a 32bit OS then install the x86.
Just another little tidbit. They are both X86, One is X86-32 (32bit and commonly known as X86) the other is X86-64 (64bit and commonly know as X64)
I hope this clears things up for you.