But when you're not playing high-end video games, most of that processing power sits idle. It's like the difference between driving your computer down the interstate at (or close to) top speed versus sitting at a stop light waiting to go. Your engine is still running, but it's not accomplishing anything.
With computers, though, that doesn't have to be the case. Those spare CPU cycles can be put to use for any of a large number of tasks, including searching for signals from aliens, simulating the folding of proteins to better understand the causes of diseases (and find potential cures), simulating weather to help create better predictive methods, search for spinning neutron stars by processing data from LIGO and GEO gravitational wave detectors, or many other projects.
The software that runs these projects is called BOINC, and it is designed to run in the background, using only the spare processing power. It doesn't interfere with your computer's normal processes, because it sets itself up to run in the lowest priority setting on your computer.
It doesn't cost you anything to run BOINC, and it may just help some advance some research project toward curing a disease or furthering our understanding of the universe around us.