I saw this at a blog, and thought it was a good question. The most interesting thing about the question is not that someone would ask it, but how you would go about explaining what we take as obvious. It's complicated!
"Common" means something, as in community, communism, comity, complicated, etc., like being-with, being-together, sharing, oneness. So in a way, just like words mean something because of common agreement, so the concepts that are formed and shared mean something, by agreement, but agreement that comes from experience. Even words aren't a matter of "agreement" in the strictest sense but have that element of experience, then we are agreeing. It's what I think of when we consult the dictionary like it's some kind of authority on words: "Who put them in charge?" But it is an authority because we, somewhere along the way, did put them in charge! That's the way it is with experience of facts, concepts, things observed, imagined, predicted, and on and on. It's all gathered together, strictly or loosely.
So just the words "common sense" I think are pretty clear: "sense" is understanding based on teaching and/or experience, and "common" is what is generally observable and seen as more or less true by people in general.