Swap files are used to swap memory pages in and out of memory. It increases the amount of memory available to programs over your physical memory by "faking" requested memory allocations with disk space.
Your "missing" disk space is because of the calculations. Disk drive manufacturers advertise a drive that contains 120,000,000,000 bytes as 120 GB. Windows (along with just about everyone else) counts that as 111 GB and change. On my computer, the recovery partition is a tad over 10 GB, leaving 99.something GB for available space on the main drive.