LinkedIn is a social network with a decidedly more "networking" feel. It was originally set up to allow people to do the sort of networking that happens at both conferences and company parties. The idea is that you connect with people you know, then if they know someone you would like to get to know, you can request an introduction. This is why the service stresses that you shouldn't link to, or connect to, people you don't actually know.
LinkedIn has a free basic service that lets you:
as well as a premium service that gives you a bit more access to other LinkedIn users. The free service, the one that I use, is good enough for most uses!
LinkedIn has, as all social networks do, a way for you to create a profile for other users to see. When you enter in all of the jobs you have held, the educational institutions you have attended and the various clubs, committees and any other ways you may have met people you would like to be linked to, you will be given a list of all of the other people who have worked in those jobs (at the same time you did) or attended those schools or belonged to those clubs/committees/etc. When you recognize someone, you can easily invite them to become "linked in" with you and they will be one of your connections, as soon as they approve the invitation. Through them, and their connections, you can grow your network and keep meeting new and interesting (and possibly helpful) people.
My LinkedIn profile is http://www.linkedin.com/in/hastingsr if you want to see a profile in action (or make me a connection of yours...).