A social network is a site that facilitates relationships between people based on common interests. Examples would be Facebook, Ning, or LinkedIn.
Typically they have more features than forums, their predecessors in community software. They make it easier for people to share information, whether personal or professional in nature, via the web.
So social networking is the use of those sites to enhance, create or deepen relationships. They can be one-to-one, one-to-many, or entity-as-one to many.
You can find more technical definitions here.
And here’s a short video on the subject that is often referenced, on YouTube.