This question is harder to answer than it appears.
At the simplest level, a social robot is one that is designed to interact with humans, in the same way as humans interact with humans.
But there are different levels of interaction. A robot that moves along the sidewalk in a way that moves with with flow, rather than causing chaos by moving like a vehicle, needs some level of social skills to be able to do this. It needs to know which side to keep to for the direction its going, and it needs to judge how fast and how erratically other pedestrians will move in the next few seconds. These are sophisticated skills; in busy cities humans don’t do so well at these.
At the next level of sophistication, a social robot needs to understand what humans are saying to it. One of the obvious benefits of social robots is that they can be instructed rather than programmed. But understanding the intent of what a human says, so that the human can sketch the desired behavior, is much harder than requiring the human to make a clear, unambiguous statement of the desired behavior, i.e. programming.
At an even greater level of sophistication, a social robot needs to understand what’s going on in the minds of the humans around it. Now it doesn’t necessarily have to be instructed; it can figure out what humans desire, without them having to express it.
To look at the media, you would easily get the impression that social robots are either very close to mass production, or at least only a few years away. I don’t think that this perception is even close to accurate. The glitzy presentations that you can find on the Web are invariably closely scripted so that the robot is just following canned actions and conversations. Roughly speaking, no social robots at any of these three levels exist today. But there are many interesting research problems, and many potential payoffs even outside the area of robotics. After all, if a social robot can understand humans, then maybe human can understand humans too.