Distributed computing uses spare computing cycles to perform calculations for the benefit of one of many scientific projects.
I originally started with Seti@Home, which has switched to new software called BOINC which can also run other projects.
The projects I currently run on the BOINC software include Climateprediction.net: study climate change, Einstein@home: search for gravitational signals coming from pulsars, LHC@home: improve the design of the CERN LHC particle accelerator and Predictor@home: investigate protein-related diseases.
I do all of the above as part of a team called The Knights Who Say Ni!, who are involved in many other projects.