Topology is the arrangement for how point, line, and polygon features share geometry. Topology is employed in order to:
If you have features that are coincident (i.e., share the same location of coordinates, boundaries, or nodes), chances are that using a geodatabase topology can help you better manage your geographic data.
Most users care deeply about the spatial integrity of their feature data, and geodatabase topologies help to better manage data integrity. Using a topology provides a strong mechanism to perform integrity checks on your data and will help you to validate and maintain better feature representations in your geodatabase.
Also, many users like to use topologies for various analytical operations (e.g., to find adjacent features, to work with coincident boundaries between features, and to navigate along connected features). Topologies enable richer analytical functions in your GIS.
Topology is fundamentally used to ensure data quality and to aid in data compilation. Topology is also used for analyzing spatial relationships in many situations -- such as dissolving the boundaries between adjacent polygons with the same attribute values or traversing along a network of the elements in a topology graph.
Topology can also be used to model how the geometry from a number of feature classes can be integrated. Some refer to this as vertical integration of feature classes.