Hibernation was designed for laptops and might not be available for all PCs. It uses less power than sleep and when you start up the PC again, you're back to where you left off. Hibernation suspends to disk unlike the sleep option that suspends to RAM. That's why it takes a bit longer to wake up from hibernation than from sleep.
Swap space is the area on a hard disk. It holds memory pages that are temporarily inactive. Swap space is used when your operating system decides that it needs physical memory for active processes and the amount of unused physical memory is insufficient. When this happens, inactive pages from the physical memory are then moved into the swap space, freeing up that physical memory for other uses.