Middleware is a great answer if you are talking to a software engineer but its like trying to explain "what is light" or "what is time". If your audience doesn't have previous exposure to the technical background details it may be better to describe what is it's effect or how is it useful.
My angle would probably be:

There is a network of people who contribute to research by volunteering some of their PC's spare computing power to solve massively difficult problems. BOINC is the backbone of that network, it's the system that links research projects with volunteers.
(You can exchange PC with phone, tablet, laptop or any other applicable device)

If that raises interest I might explain how a big problem is broken up into little parcels of work and sent out to millions of volunteers, also, when the results are combined the network of volunteers can outperform a supercomputer.