LinkedIn has opened a new Volunteer Marketplace on its website. This is US only at the moment, but it will help you find volunteer opportunities and positions in your area.
If you're using LinkedIn to list your skills and work history, then having volunteer experience at a non-profit organization will help fill out your profile. Not only is volunteer work good for the community, it also can give you a better advantage when applying for paid positions.
LinkedIn has been working to attract younger users to the network. For instance, they've added university pages and lowered the age to sign up to 14. Offering volunteer opportunities like this is another way to bolster that effort, since many students are looking for ways build up their resumes.