Win32 runs 32 bit programs on 32 bit processors and provides legacy support
for 16 bit programs.
Win64 runs 64 bit programs on 64 bit processors and provides legacy support
for 32 bit programs.
Some examples of 64 bit processors:
Intel Itanium
Newer Xeon
AMD Athlon 64
Some examples of 32 bit processors:
Just about everything else