In a nutshell, a dual-core processor allows for better multitasking than a single core processor, because two threads can be processed simultaneously.
A dual core processor will not provide exactly twice the clock speed (a 3 GHz dual core processor does not effectively give you 6 GHz). However, in general, dual core processors can provide performance that is close to twice the clock speed of a single core processor at the same speed.
Originally Posted by Vowen
...Or does it mean that I can run two 3.0 GHz programs simaltaneously?
In a multitasking operating system like Windows XP, you can already run two programs or more simultaneously, albeit maybe slowly.
A dual core system allows multitasking with better performance.