It resides on one or more chips inside the computer. Each chip is a grid of silicon wires encased in a plastic container about the size of a fingernail. It functions the way your brain functions, coordinating the activities of the other devices. Other chips along with the CPU are RAM chips and ROM chips.
RAM chips are always blank when the electricity is off.
When people refer to a 64K computer or 128K computer, they are referring to the size of the RAM capacity. On an Apple II computer, some software packages require 128K and not just 64K in order to work properly, because the program takes up a lot of room. ROM chips are crucial to the computer, but not very interesting to you as the consumer. A ROM chip typically contains frozen information that the manufacturer wants accessible at all times, independent of disks. On the old ADAM computer by Coleco, word processing was frozen into ROM so it was automatically capable of word processing when you turned it on.