Why is CPU important to the computer?

The CPU is the main logic chip or "brains" in the system. It is what runs all of your software, and it is required for the computer to do anything at all. It is the "brains" regardless of whether an operating system or other software is installed. Even without the OS, you have the BiOS, EFI, or other firmware that gives it the ability to configure core system hardware and the ability to load an operating system.