Dual-core processors, or more correctly
multi-core processors (for you can have more than two) essentially integrate the 2 (or 4, or whatever) processors onto a single processor chip.
This allows programs to truly multi-task, but unless the OS or program is written to handle this correctly, you won't notice a performance improvement.
We currently have an issue at work where our RAD tool (PowerBuilder 10.5) does not support this new technology, and it appears that it will not do so for the immediate future. Therefore, customers purchasing machines with dual-core processors will not observe an improvement in performance if all they are using it for is PowerBuilder products. However, if the OS (and other concurrently programs) so, then there will be an improvement, even if it's only small.
There is a Wikipedia descripion of multi-core
here.