A swap partition is akin to the page file on Windows. The kernel will use it to move memory pages it doesn't anticipate using in the near future to it so it can use that RAM for other things. It will also use it in a pinch when there isn't enough RAM on the system. It isn't strictly necessary, but it can prevent programs from crashing at a huge performance penalty. It is necessary if you want to use sleep or hibernate or whatever it's called when it is powered off physically but resumes what you were doing instead of booting when you power it back on. That takes as much swap as you have RAM at minimum. If you want that, a good rule of thumb is 1.5 times physical RAM.

I have servers I administer for my job that have over 100GB of RAM with very little swap, like 4GB. The applications and machine are tuned and sized so the physical RAM is at ~85% and swap is barely used. The swap is mainly for non application stuff like IDS agent, backup agent, monitoring agent, etc.

If swap becomes a problem, you can adjust the kernel vm.swappiness parameter as needed. It might take some trial and error to get it right.

Source: I've been working with Linux professionally for almost 20 years now.