In a plain, non-technical english nutshell :
Improved Performance.
Basically it allows your system to be more efficient. The more temporary stuff it can store in RAM rather than on the Hard Drive, the better.
(not massive... more RAM generally renders a "snappier" feel... assuming you haven't got a Celeron or other cheaper bottleneck processor and a relativley tidy system i.e. not too much fragmentation or rubbish running in the background)
For your average Joe, 2GB should be a good target value to have in your PC. If you're a gamer, like playing with photographs, complicated spreadsheets or other stuff.... then 4GB on Windows, will probably be just fine. If you're on a Mac and want to leave VMWare/Parallels running Windows in the background then your wallet and motherboard tech spec is the limit, because you'll need to consider the memory requirements of your Mac as well as any virtual machines you want to run.
Computer performance priorities (hardware, in order of preference) :
1. Processor (slow processor....forget anything else)
2. RAM
3. Graphics Card (only of concern if you are a gamer or graphics heavy)
4. Hard Drive (for most people, focusing on a tidy, defragged OS would be more worthwhile than messing around with Hard Drive upgrades)
For any more info.......
"extra ram benefits"
into your favourite search engine.