How does dual processing work?

there are two things you may be talking about here as the two are often confused:

1. Dual processors. in which case, there are 2 separate processors on the motherboard, effectively doubling the computing capacity. There are very few motherboards and cases that support this but one that does is the Mac Pro from Apple. Using dual quad core processors, the computer can utilize up to 8 cores.

2. Dual core. in this case, there is one physical processor which is essentially split in half. this allows the computers to process 2 things at once whereas single core processors can only do 1.