Grid computing is the concept whereby complicated computations are broken down into smaller tasks and the tasks are shared amongst a network of computers. This model allows individuals to contribute to a larger project by volunteering processing power to complete a shared task. You can read a more thorough definition at Wikipedia.
SETI@home (Search for Extraterrestrial Intelligence) is the largest example of grid computing with over 3 million users downloading and analyzing radio telescope data with the aim of discovering a signal that is proof of intelligent life.
LHC@home is a similar project developed by CERN to help them process and compute the 15 petabytes of data the LHC will produce each year. To join, you can follow the instructions provided on their site. You will need to download some software called Boinc to participate.