Union is an overlay feature and analysis tool found in the overlay toolbox with several other useful tools, (e.g. Identity, Intersect,etc.). Union is a tool that can only be used with polygon features. It takes the two polygon features and combines both the spatial polygon and the associated attribute data into a single, composite layer. This allows for analysis of two datasets information together in one layer.
To simplify, union in GIS terminology means the same as it does in any other terminology; 'to put together'. In map making, two different sets of information or layers can be put together into a single set using a union operation. This can be done with most mapping software systems in an internal algorithm that takes the two layer inputs and outputs a composite of the two. An example of when this can be used is in analyzing the habitat of many different animals. In this example, if you have an area that is inhabited by elk, deer, and antelope, you could take the three sets of habitat information, use a union operation on them, and have an output of total game animal habitat for that area.
Union is particularly valuable in map algebra and allowing the cartographer to do suitability analysis.