Is it the processor? Or maybe RAM? I'm sure, it's not the GPU though. Which and what part does it make them powerful to mine?
Bitcoin miners have ASIC (application-specific integrated circuits), special chips which can perform mining calculations and nothing else, and are very efficient for it. The specific calculations required are encoded in the hardware - the transistors are arranged in the pattern "calculate SHA-256".
In contrast, the CPU that exists in normal computers can do everything, but is not very efficient at any one task. The transistors are arranged in the pattern "execute the instructions that you are given". So you can give it any instructions you want, including "calculate SHA-256" - but it will not be as efficient as a special-purpose chip.