You can tell someone important information using a lot of numbers, but you're liable to put the majority of your audience to sleep. Showing people the relationship between those numbers without having to do even the simplest math is way more effective, and that's the value of graphs and charts. Presenting dry data in visual form can make a trend very clear when the numbers don't, and sometimes those visualizations have an impact that changes the world.
The Royal Society shows us how these charts and graphs made information available to many more people than would have otherwise learned of the data they contain. Of the five examples explained here, I had only never heard of the fictional Kallikak family tree, used for nefarious purposes. But as soon as that section began, I thought of the family tree at the beginning of the movie Idiocracy. Also fictional, of course. -via Kottke
See also: Florence Nightingale’s Statistical Diagrams and John Snow's Cholera Map.