A core is just a processing unit. Information is sent to a core, and the core deciphers the instructions and performs the appropriate actions.
More cores means your computer can process more calculations/handle a higher 'work load' in a sense. That said, not all cores are created equal.
Some cores are hyperthreaded (can perform multiple 'actions' on one core), some are not. They have different clock speeds, which is the best thing to compare when looking at chips with the same architecture. Then again, different architectures can be misleading. An older chip that may have a higher clock speed may perform worse than a new one with a lower speed, because it's not just about clock speed, but what the chip can do in a cycle.
The best thing to do is to look at benchmarks. Something like this:
PassMark Intel vs AMD CPU Benchmarks - High End. Find out what processor you're looking at and it gives you a rough idea of where you're at compared to other ones.
If you're looking at VPS's, they often express how much power you're getting in 'cores'. Make sure to check if those cores are 100% yours, or shared. See what processor they're using for your server. See if they are talking physical cores, or virtual cores (they like to do that to trick people into thinking they're getting twice the processing power than they actually get).
That said, 4GB of Ram will run you somewhere between 8-10 OSRS clients (depending on OS, client, etc.). It's not really a number of cores to look for, but rather an amount of processing power.
