Swap is the same thing as virtual memory on windows OS. In a nut shell ( in reality its a little more complicated ) if you run out of physical ram, non active applications and data will be exchanged between RAM and the hard drive.
I think having a swap partition is a good idea. The 2x rule IMHO is outdated with lots of RAM. A 512 partition is a good size.
The console command free will tell you if swap is active. If total swap size is a non zero value its working.
Using swap space is slower since your using the hard drive. And in most cases unless your PC is a hard core web, mail and or database server it probably will use little or no space at all. If you need swap and do not have your machine will really slow down and it might crash.