4 cores = more grunt in modern games.
4 cores = more threads available for multi-threaded applications (see the above point).
Your OS should do it automatically, but imagine assigning a program/process to a particular processor. With a single core, they all used to have to go through the same CPU sequentially. On multi-core CPUs, there are multiple processors to run multiple applications at the same time (kind of parallel processing as @FireMadeFlesh mentioned).
In a scenario where you are running a game, one core could handle the AI programming, another the physics of the environment, another the interface between processor and GPU, etc…. – games like Bad Company 2 or Crysis 2 take advantage of this potential; older games do not.
As @FireMadeFlesh said, CPU manufacturers check the CPUs they produce for the clock speed they are capable of running at the stock voltages of the chip. If they chips can’t achieve the speeds, they CPU is raped down and it is checked again until a stable clock speed is found for the voltage going to the CPU. This is called speed binning. This thread on Anandtech has some useful info and a video.
If, on a multi-core chip, a disparity between the maximum speeds of the cores becomes apparent, they will deactivate the under-performing cores and sell a 4x core as a 3x core, while giving the buyer an opportunity to unlcok the cores. Often, a slight increase in voltage above that which the chip was designed for will allow for workable clock speeds on all the cores that don’t cause blue-screens and the like.