LinkedIn is a professional social media network. It works in a similar way to Facebook in that you have a profile and you decide how much of your profile you want to show to other people, and someone who is looking for you might put your name in a search engine and get connected to your LinkedIn page.
However, unike Facebook and other networks of that kind, it is much more geared towards work. People typically put their work experience on the site, and if you have a reference from a previous client or employer it is now very common to ask them to put this straight on to LinkedIn. You can also endorse other people for their skills, though as people tend to endorse their friends it is questionable how much value this has - unlike a recommendation which is very useful.
You can get an idea of how LinkedIn works here.