32-bit means the OS is 32-bit architecture vs. 64-bit, which 64-bit architecture.
-- Some older programs (mostly pre-WinXP) will not run on 64-bit architecture.
-- Most programs will run on 32-bit OSes.
-- It is difficult to find 64-bit drivers for older hardware because most hardware (printers, scanners, etc.) manufacturers won't write new 64-bit drivers for their old hardware.
-- 32-bit Windows cannot see and use more than ~3.5 GB of memory, while 64-bit Windows can see and use more memory than most computers can physically handle.
-- You should backup your data files and any special files you want, e.g., your Mozilla bookmarks, so you can copy them back into your new OS and "My Documents" folder.
-- Not sure what it would "cost" to change your OS, depends on whether or not you have an OEM, Upgrade, or Full Retail installation disk.