If I were to skip straight to the part in The Shawshank Redemption when Andy Durfesne climbs out of the pipe of poo (and put it on mute), someone who never saw the movie might see an escaped convict who steals money from a warden and fleas to some random place in Mexico called Zihuatanejo. Out of grief, the warden kills himself and Ellis Boyd "Red" Redding eventually teams up with Andy to commit more crimes.
Those of us who have seen the movie though know this isn't the case. Why? Because we saw the whole movie and have context.
As Andrew, a FlowingData reader, put it, "For statistics to be useful, it needs to be explained in a context." When I get my hands on some data, whether I'm analyzing or visualizing, I want to know the context of data first. I want to know who collected the data, how it was collected, when it was collected, and what was done to it before it arrived in my hands. Without that meta-information, I could easily make an incorrect assumption about the data or misrepresent it somehow in a visualization - which is very bad.
Simply put, we use visualization and statistics to tell stories with data. If we don't have all the information, then we can't tell a complete story.