Topology in GIS describes the spatial relationships between vector features (how they connect, share boundaries, and enclose space) independent of their exact coordinates. It also refers to the rules that enforce those relationships so a dataset stays geometrically valid: polygons that should tile a map have no gaps or overlaps, lines that should connect actually meet at shared nodes, and features that should be contained truly are.
Why it matters
Clean topology is essential for trustworthy analysis. Geological unit polygons that overlap will double-count area; gaps (slivers) between them create false NoData zones; fault lines that almost-but-don't-connect break network and adjacency queries. Topological errors propagate silently into every downstream overlay, dissolve, and area calculation.
Concrete example
In QGIS, the Topology Checker and Geometry Validity tools flag rule violations such as "must not have gaps," "must not overlap," and self-intersections (a common cause of invalid geometries). In PostGIS, ST_IsValid(geom) tests OGC validity and ST_MakeValid(geom) repairs many problems. Snapping vertices to a tolerance during digitizing prevents most gap and overlap errors at the source.
Common pitfall
Confusing topological validity with simple geometric correctness, and confusing this GIS sense of "topology" with network topology in IT. A self-intersecting "bow-tie" polygon may render fine but returns wrong area and can crash overlay operations. Validate geometries before analysis rather than after results look wrong.