GIS is much more than mapping software. GIS is a technology that can change an organization fundamentally and positively. Most computer technology is designed to increase a decision maker's access to relevant data.
GIS goes beyond mining data to give you the tools to interpret that data, allowing you to see relationships, patterns, or trends intuitively that are not possible to see with traditional charts, graphs, and spreadsheets.
More than that, a GIS lets you model scenarios to test various hypotheses and see outcomes visually to find the outcome that meets the needs of all the stakeholders. For example, a city employee looking to build a fire station can analyze the locations of other stations in relation to potential locations in a spreadsheet view. GIS lets that employee visualize potential locations on a map along with drive-time analysis, environmental concerns such as wetlands that might hamper construction, or any number of siting criteria that would be too cumbersome to comprehend otherwise.