A lot of information can of course be found on their website http://www.worldcommunitygrid.org :

• The mission of the World Community grid
• How Grid Computing Works
• List of active (sub)projects, at this time of writing the list is :
• Drug Search for Leishmaniasis  
• Computing for Clean Water  
• The Clean Energy Project - Phase 2  
• Help Cure Muscular Dystrophy - Phase 2  
• Help Fight Childhood Cancer  
• Help Conquer Cancer  
• Human Proteome Folding - Phase 2  
• FightAIDS@Home  
• List of completed (sub)projects

BOINC is a kind of "universal program" that allows your computer to run task dispatched by the servers of the projects you decided to participate to. BOINC stands for "Berkeley Open Infrastructure for Network Computing". It's free and open source software.

A project is a given computing task, for example "check if this number is prime".

BOINC will connect your computer to the project server(s) : it'll contribute to a grid.

It's a computer / server / network type of connection. In a grid you have a centralized main server which send tasks to the connected computers ("clients"). When a tasks is accomplished by a client, the results are sent back. The clients don't connect to each others (that a peer to peer architecture). The grid exists as long as the server asks the client to process data for a project. A grid runs one or many (sub-)projects at the same time for the achievement of a global task (e.g. find the largest prime number).

Clients are often geographically dispersed and are of different type (eg. PC's running Windows or Linux, MacIntoshes, servers, etc.).

"World Community Grid (WCG) is an effort to create the world's largest public computing grid to tackle scientific research projects that benefit humanity" (Wikipedia). Project will focus on scientific or medical research.

It probably won't. You can easily change the parameters of BOINC using the (included) project manager. For example you can tell BOINC to stop all tasks if the processor usage becomes higher than a given value. If this value is low enough BOINC will run intermittently (for example during the time you read these lines, but will stop as soon as you start scrolling down the page). Also you can limit the processor usage to a given value (eg. 60%) and the number of the cores to use (in case your computer has a multicore processor).

The default settings of BOINC running the World Community Grid sub-projects are very conservative already.

That won't happen because your computer will never been accessed from the Internet. It's the exact opposite: your computer will connect to the highly secured IBM servers to download tasks (small data files, for example .png images). When one or more tasks are completed your computer we'll again connect to the servers and send the results back, it'll probably use the same connection to fetch more work.

To join this project you need to follow 3 steps:

1. Register on http://www.worldcommunitygrid.org
2. Download and Install BOINC
3. Run BOINC and attach it to the project and team.