But your system may not have 4 GB. So the operating system has a data structure called a page table that has the virtual to physical mapping for each process. The processor accesses this table (it caches it in something called a TLB) so that it can convert the virtual address to the physical address.

An example using small numbers. Your program has a pointer to data. That pointer may have value 800. Let's assume that the amount of memory on your system is only between 0 - 400. So the processor has to convert the value 800 to a value between 0 - 400. It's the operating system's job to maintain that valid mapping.

Why does this matter, and why is it so tied up with paging to and from disk? Let's say the OS pages out the page containing that data. Then, later, it's paged back in, but in a different physical location in memory. Your program still has the pointer value 800, but your program still works correctly because the operating system keeps track of where in physical memory 800, for your process, maps to.

People in the Windows world often say "virtual memory" when they mean "swap space" because Windows would call the amount of swap space "virtual memory size." But virtual memory is the technique described above. Read the Wikipedia entry from above, or read an operating systems textbook for a full discussion of it.