Modern computing employs 'multi-tasking' and has done for years. Basically, we're doing multiple things on a computer at once, and the time of the processor is being sliced up and allocated to each application by priority.
Historically this has meant that things slow down notably if one process is eating up a lot of processor time.
Dual-cored processors (and dual-processor systems) have made for truer multi-tasking. Applications that are bound to a single core will no longer be able to steal processor time from other applications running on another core. Applications are quickly being written to take advantage of multiple cores, which can almost double the speed of execution of some processor-intensive tasks, which may negate this advantage somewhat in favour of faster per-application performance.
In the simplest terms, having multiple processor cores is advantageous. Just bear in mind that an application that is bound to a single core will only execute as fast as that core will allow it. As such, a slower-clocked dual-core processor would be slower than a faster-clocked single-core processor. However, given that modern computers hardly ever run a single CPU-intensive process this shouldn't be much of an issue.