Distributed Computing is the practice of breaking up large computing tasks and, well, distributing them across several computers. More specifically, it refers to programs where master projects use code such as BOINC (Berkeley Link) to distribute those tasks across hundreds of thousands or, potentially, millions of computer CPUs, GPUs, and, in some cases, PS3 game consoles, in order to make possible operations that used to require dedicated supercomputers for a fraction of the cost. This works because, while your day-to-day operations might be very taxing to your computer (chances are they aren't), your computer actually spends a lot of time idling, unless you are judicious about shutting it off when you aren't sitting in front of it. When you are idling, you're typically only using about 1% of your CPU's total processing power. Distributed computing programs take advantage of that idle time by performing (with your permission, obviously) operations on your CPU during your down time.
System requirements are going to vary from project to project, but for the average computer, it's not a bad way to be idling, if you're going to leave it idling. Hell, if you're anything like my, your processor is functionally idling most of the time anyway: the occasional very large excel file might cause a bump, but apart from gaming, my system runs pretty flatly at about 5% of capacity, even when I'm using it. Burning just as much power, mind you, but wasting it. If I were to tap into that unused processing potential, all of those billions of calculations-per-second could contribute to solving problems for real people. I've seen everything from using your processing power to help animators do 2D and 3D rendering, to performing analysis of chess games, to helping cull SETI data to look for extraterestrial life.
Some of this stuff has serious applications in molecular biology and, by extension, medicine. I strongly suggest all my readers look into it and see if they can find even one project they are willing to let use some of the calculations they were just throwing away anyway. Whether you want to look at it as an act of charity, an increase in energy efficiency, or Living In The Future is entirely up to you.
Me? I'm going to be running Milkyway@home, Orbit@home, and Folding@home. Processing power permitting, of course.