Good visualizations show trends that would take longer to discover by reading the numbers. They're a lot more user friendly, too.

I think they're a great communication tool between the technical people and everyone else, and it creates a simpler dialog. "Why is there such a big drop in the graph here" "Well, our traffic was lower because..."

I think it's also an emotional/psychological thing. Business people like to see upwards trends! It makes them more confident in the business.

etc. I'm sure there are far more qualified people to answer this.