Having seen data visualised, an appropriate set of questions can be formed which leads to better understanding. The human mind processes and analyses visual patterns many orders of magnitude faster than it can handle numbers. Only once a basic understanding exists, algorithms can be intelligently applied to quantify and refine that understanding. Understanding that comes from visualisation can give your organization the competitive edge. Data mining is just that - searching though mountains of data to find the important values, the critical relationship.
Visualisation is a powerful tool to quickly analyze millions of numbers in the blink of an eye.
Often visualisation is thought to mean sophisticated, multi-dimensional graphics. Certainly it can mean that, but not always. Some data is genuinely best displayed as a line graph for example. By the same token, some data is only displayed as line graphs because more powerful techniques have not traditionally been available. Users become comfortable with what they know and don't think beyond what they have.