Regardless of what type of computer you have, whether it be a desktop or tower or laptop, at the heart of it is the microprocessor. The microprocessor, more commonly known as the Central Processing Unit (CPU,) is an entire computation engine housed on a single computer chip. Prior to the microchip, computers were built from either collections of chips or transistors wired one at a time. The first microprocessor ever released, the Intel 4004, operated at only 4 bits at a time. Typically, processors today operate at 32-bit, and newer processors are even operating at 64-bit, increasing efficiency.
A microprocessor executes a collection of machine instructions that tell the processor what to do. Based on the instructions, a microprocessor can carry out 3 basic tasks. Firstly, using it's ALU (Arithmetic/Logic Unit,) a processor can perform mathematical operations such as addition, subtraction, division, and multiplication. Secondly, a processor can move data and information from one memory location to another memory location. Thirdly, a processor can make decisions and jump to a different set of machine instructions based on those decisions to carry out another task.
One thing that needs to be taken into account is the chipset of the processor. The chipset of both the processor and the motherboard must match for them to be compatible. The two main processor manufacturers, AMD and Intel, use different chipsets. Within both companies, however, they also have multiple chipsets which generally change as they introduce newer, more efficient processors. For example, 32-bit processors will not work in a motherboard designed for a 64-bit processor chipset and vice versa.