I'm not 100% sure I understand what this question is asking, but if taken literally, there is at least one thing one can do to improve a computer's CPU (the central processing unit)--the brains of your computer.
You can "overclock" your CPU. Most commercially rated CPUs are tested to run at some clock speed like 2.8 GHz. The higher the speed, the faster the processor, and thus the faster the CPU can compute things. Some BIOS allows for changing the clock speed.
Unfortunately, there is a price for overclocking. Provided you are able to overclock your CPU (through some BIOS setting), and your computer doesn't become unstable, you may have to cool the CPU. You see, when you push a CPUs clock, it tends to generate more heat. There are products that will allow you to do this.
This is what a tinkerer might do, but normal people should just buy a new and faster computer if they think their old one won't cut it anymore. However, there are some things you can do to make your old computer run faster.
If you want to see what you can do to make your computer go faster, check out my hub on Understanding Computer Performance Fundamentals (http://goo.gl/yYRN7).