A Coordinate Reference System (CRS) is the framework that ties numeric coordinates to actual locations on the Earth's surface. It bundles a datum (a model of the Earth's shape and its origin/orientation), a coordinate system (the axes and units), and — for a projected CRS — a map projection that flattens the curved surface onto a plane.
Geographic vs projected
A geographic CRS expresses positions as latitude and longitude in angular units (degrees) on an ellipsoid — for example WGS 84 (EPSG:4326). A projected CRS expresses positions in linear units (usually metres) on a flat plane — for example a UTM zone such as EPSG:32633 (WGS 84 / UTM zone 33N) or Web Mercator (EPSG:3857). Geographic CRSs are right for storing and exchanging global data; projected CRSs are right for measuring distance, area, slope, and buffers.
Why it matters
If two layers carry different CRSs, they will not overlay correctly until one is reprojected. Worse, doing length, area, or slope calculations directly in a geographic CRS produces nonsense, because a degree of longitude is not a fixed ground distance — it shrinks toward the poles. Always know your data's CRS, declare it explicitly (no "assumed" CRS), and reproject to an appropriate projected CRS before analysis.
Common pitfall
Confusing "assign a CRS" with "reproject." Assigning a CRS just labels coordinates with a definition; reprojecting recomputes the coordinate values. Tagging WGS 84 data as Web Mercator does not move the points — it mislabels them, and everything downstream will be wrong. Always confirm which operation a tool is actually performing.