I've though a lot about this particular question because I get asked it a lot, so mcu so that I started coming up with a stock answer. I decided the easiest way to explain social media was to say that it was any interaction over the internet between more than 2 people at a time. Like I said it's a stock answer and not anywhere near correct.
When I was trying to convince my Temple an work to get more involved in social media for their own good, I came up with different definitions.
For my synagogue I suggested that social media was first and foremost about creating community. The Social part of social media is what makes it important and useful. Part of any religious organization is about creating and fostering community. If there is a tool to help that goal along, we should use it. So far we haven't adopted anything beyond linkedin and facebook, but we're getting there.
At work I stressed that social media is a way of communicating interactively with the most important people to us, our donors. The money angle did get a reaction adn although I've gotten only permission for establishing a couple of accounts, including a test twitter account, I have high hopes.
Social Media is all of these things at the same time. It allows us to connect to others, to establish and develop community and to express ourselves. All of this involves very little cost, just the time put in.