Probably have to explain what distributed computing is first. Like...massive expensive supercomputers with hundreds of thousands/millions of CPUs, GPUs, etc. are used by major governments for massively computationally intensive tasks such as weather forecasting and climate modeling, nuclear bomb simulations, molecular simulations, drug discovery, protein folding, big math problems, big physics and astronomy problems, economics and finance, etc. These supercomputers use megawatts of power, cost millions of dollars to build and maintain, and take up a very large room. Reference the Top 500 Supercomputer Sites website that keeps track of all the publicly known fastest supercomputers in the world.

Then segue into what distributed computing is, where it's similar in that many CPUs or GPUs all come together to tackle a massively intense problem in the same disciplines: drug discovery, molecular simulations, protein folding, weather forecasting and climate modeling, math, physics, astronomy problems, etc. but don't require fast interconnects or "identical" hardware. But distributed computing is different than a traditional supercomputer in that it's ok for the individual CPUs to not be able to talk directly with each other; i.e., there's nothing time sensitive, so it's OK if hours or days go by. The centralized server takes all the tiny pieces and puts them together into the solution. (I don't get the magic behind this.) In other words, both supercomputing and distributed computing are examples of parallel computing, but the former typically requires fast interconnects and specialized, identical hardware, whereas the latter doesn't require fast interconnects and can run on commodity hardware.

For all intents and purposes, distributed computing projects allow the average Joe or average Jane to use their own personal computer to download a bite-sized chunk of a problem to crunch, then send the results back, then ask for more work. Over time, thousands of volunteers using thousands/millions of computers can achieve similar computing power as the big supercomputers, all using their own volunteer computers and volunteer electric bill for "good" or "interesting" projects. Many research projects in academia are strapped for cash and dependent on government grants and charitable donations to survive, or otherwise the projects have to close or not get off the ground. Distributed computing provides a "free" charitable "supercomputer" for researchers to use for their research simulations and modeling. Also emphasize that most of the big distributed computing projects require results to be published and public domain.

Could probably walk through a history of distributed computing. I remember in the 1990s three big projects:
1) Distributed.net - RC5 encryption cracking as a proof of concept on encryption strength
2) Great Internet Mersenne Prime Search (GIMPS) - finding larger and larger Mersenne prime numbers
3) Berkeley Search For Extraterrestrial Intelligence (SETI@home) - radio astronomy analysis to look for signals that may be indicative of another lifeform trying to communicate. This project set the groundwork for the development of the BOINC platform at Berkeley.

Another popular distributed computing project (from the early 2000s I believe) is Folding@home - Originally founded at Stanford but now hosted at Washington University in St. Louis. This uses its own platform and software but tackles protein folding and misfolding for Alzheimer's, Parkinson's, Huntington's, several cancers, and many other disease targets.

With respect to BOINC itself, you can refer to the BOINC Projects List to get an overview of all the math, science, etc. projects available. If the person is already a science buff, there should be enough information there as well as the websites of the individual projects to understand what each project hopes to achieve. Pictures on the websites can help too. Screenshots of BOINC overall and the fancy project graphics can help too. Maybe emphasize that distributed computing projects don't require any expertise on the volunteer, just a willingness to run the program on their computer, and it's "set it and forget it" and simply quietly works in the background.

There's many ways to introduce the topic depending on the person's background. I do share your pain, as I bet there are hundreds of millions of computers just doing nothing, and I bet less than 1% of people even volunteer -- heck, maybe 0.1%! If more people "understand," I bet we can cure some diseases several years faster.

It is unfortunate that most people are switching from desktop to laptop computers, so heat and battery life are concerns as well as most laptops aren't built for 24/7 usage. And heck, many people are moving to tablet and phone computing, even for all their banking and entertainment. Even laptops are peaking. We could probably target the gaming and PC enthusiast communities, as these people already understand "computers" but just need to be introduced to distributed computing. It's very easy to take 10 minutes to download and install a program and create an account.

We almost need marketing dollars to go towards YouTube ads or something to spread the word on WCG and other big projects. I mean, every sane person hates cancer, no? I bet YouTube, Facebook, TV and radio, etc. ads could help get the word out even more than existing Facebook, Twitter efforts. And maybe some "free" spots in big newspapers and magazines...New York Times, CNN, ABC, Fox News, Wired, whatever.

@jringo_, I got your e-mail and replied but haven't heard back yet.

A workaround for this is to create a throwaway email address that you only use for a specified purpose and then abandon. My guess is there are probably millions of these floating around. I do not know how the email vendors deal with these or if they purge them periodically. I don't know if it is possible to set up an email account which only remains active for a specified time and then self-destructs, but if there isn't one, why not ?
Cheers