There’s an excellent explantation of virtual memory over on superuser.
Simply put, virtual memory is a combination of RAM and disk space that running processes can use.
Swap space is the portion of virtual memory that is on the hard disk, used when RAM is full.
As for why 32bit CPU is limited to 4gb virtual memory, it’s addressed well here:
By definition, a 32-bit processor uses
32 bits to refer to the location of
each byte of memory. 2^32 = 4.2
billion, which means a memory address
that’s 32 bits long can only refer to
4.2 billion unique locations (i.e. 4 GB).