In a nutshell, BOINC will use your device's idle processing power (when you're not using it, of course) to perform analysis and computation on tiny chunks of data related to medical or technological research. Once the processing is complete, BOINC will return the results to The Mothership, where they'll be combined with results from all of the other devices participating in the program. The tiny chunks will add up over time, and perform research on a much larger scale than would be possible with just a single computer or even cluster. You'll receive credit/points for each chunk of data that you successfully process and return. By joining the AF team, those points will be combined so we can see how much good we're doing together.
Does that help any?