(I wrote a big mash-up of my thoughts after seeing Sherlock Holmes last weekend, but I realized as I was finishing it up that I didn't want to post it anymore. So now you get the lazy post.)
sound practical judgment that is independent of specialized knowledge, training, or the like; normal native intelligence."
So this would be things like 'if you put your hand on a hot stove, it'll get burned' or 'don't run with scissors'. It implies a comprehension of cause and effect based on life experience. A normal adult would be expected to know these things, however children are often (repeatedly) told not to do them because they haven't fully grasped the idea of "effect" yet. These examples of common sense are ones that hopefully become adopted as children grow older and gain things like empathy and the ability to anticipate. 'Cause nobody wants to have to tell their 40-year-old brother to quit jumping on their new couch in his muddy hiking cleats.
There is another meaning to the term that most online dictionaries don't have (and it therefore falls into the arena of this blog-- popular culture), and it involves truth in contrast to commonly held beliefs. If you break down the term, "common" implies something that is widespread, ordinary, or shared by a group of people, and "sense". In other words, it's often used to describe an idea that is commonly held to be true amongst a certain group of people, regardless of the actual truth or validity of it. For example, the prevalence of what's called "scientific racism" in the United States prior to World War II-- the use of so-called scientific theory to explain why certain races were intrinsically superior to others and therefore deserved dominance over them.
Here's an old illustration from Harper's Weekly "demonstrating" the supposed similarities between the Irish and the African races, and their contrast with the Anglo race. The caption is difficult to read, but the basic gist of it is that the Irish were descended from African people who had migrated up to Europe through Spain and eventually arrived in Ireland where they bred with indigenous people there-- who were "low types", descended from the "savages from the Stone Age"-- and were subsequently isolated from the rest of the world, no longer part of the process of natural selection, and therefore inherently inferior to the anglo race from the rest of Europe. It seriously says "made way for superior races" in the last line.
Now, clearly this has no bearing whatsoever in scientific fact (I love that the author evidently believes that there are races that didn't descend from the stone ages), and is an excuse to justify the "common sense" that Africans and the Irish were naturally inferior beings to white Europeans (who weren't Irish). Implicit in this is the "common sense" that Africans are inferior-- that didn't even need to be explained in the text, the author assuming the readers would already understand that as a fact. I have seen other illustrations that supposedly demonstrate how much closer Africans are to apes than other races are, but it's the same basic concept as this one focusing on the Irish. It's the presentation of speculation in an attempt to justify a personal belief based in the common sense of the time (that darker races were naturally inferior to lighter and non-Irish ones) with little to no basis in scientific evidence. (In fact, many scientists today believe that race is a social construct, not a scientifically quantifiable category.)
So to summarize, common sense can be a good, useful thing (don't try to talk while drinking a glass of water), but it can also stand in the way of critical thinking. If people in the past had adhered strictly to common sense ideas, those us us living today wouldn't know about plate tectonics, the age of the Earth, evolution, psychology, chemistry, physics, and countless other advances in our understanding of nature.