Hi and Welcome to ItsAllPC!
RAM is your fast and furious speed demon of storage. When you CPU is functioning, it needs a place to store and recieve large pieces of data that it processes. To put it into perspective, when you open a game, the program might tell the processor to get all the geometry and textures from the slower hard drive, and dump it into memory so it can be accessed quickly when it is needed. I'm pretty sure this is where the loading screen would come into play. RAM is similar to your Hard Drive, but even if you could write this needed temp data to a hard drive, it is much slower in comparison. If you actually run out of RAM, due to a lack of RAM - as in your processor needs to store more temporary data than you have the RAM for, then it will write it to "virtual memory" which is basically a chunk of your hard drive that pretends it is RAM. The problem is that this is extremely slow when comparing to RAM and will result in your system chugging along. That is what you want to stay away from.
It's a misconception that the more RAM you have, the faster the computer will go. This is only true up to a certain point. The performance of a computer would probably not be noticable between something like 4gigs and 2 gigs. You would, however, see a difference between 256MB, or 512MB, and 1GB. This difference in performance actually depends on what you do with your computer. For the average internet/email user, 512MB is plenty, depending on the number of programs the user has running at the same time. For moderate to heavy gaming with games like Half-Life 2, or F.E.A.R. (I think), it is important to have at least a gig of RAM. This doesn't necessarily mean that if you get 4gigs, the game would go 4 times faster than 1 gig. It doesn't work that way.
For video editors, image editors, CAD, and other power-user apps, you also need a significant amount of RAM. Something closer to 2gigs+
I personaly can say that the gaming performance for my computer did jump significantly when I upgraded from 512MB to 1GB of RAM. Current gen, and last gen games generaly don't increase in performance with more than a gig, with a few exceptions. Hopefully that info is correct! Hope that helps.