The dual core system (or dual processor system - the differences are minimal in this context) will work just like a single core system on games & programs that aren't multi-threaded.
If a program is multi-threaded, then the program will run up to twice as fast (depending on the efficiency of the multi-threading of the program) on your dual core system than on a single-core system of the same clock rate.
If you are running multiple programs at the same time, say for example downloading a file, running a virus scan and playing a game all at the same time, then a dual core/processor system will make a lot of difference because its like having 2 computers available to do all that - it plays the game using one core/processor and the other one does the other stuff (download the file and run the virus scan) instead of interrupting your game to do that.
The disadvantage of dual cores is that they dont' run as fast as their single-core counterparts - Intel dual cores run at 2.8 to 3.2ghz, but you can get a 3.8ghz single core. For today's (not multi-threaded) games, you get better performance on the faster single-core than you do on dual core.
Mike.