A reference ellipsoid is an oblate spheroid — a sphere flattened at the poles — used as a smooth, mathematically defined approximation of the Earth's shape. It provides the surface against which latitude, longitude, and ellipsoidal height are measured, and it forms the geometric core of every geodetic datum.
How it is defined
An ellipsoid is specified by two parameters: the semi-major axis a (the equatorial radius) and either the semi-minor axis b (polar radius) or the flattening f = (a − b) / a. The widely used GRS 80 ellipsoid has a ≈ 6,378,137 m and 1/f ≈ 298.257222101; the WGS 84 ellipsoid is nearly identical. Earlier ellipsoids such as Clarke 1866 (used by NAD27) were fitted to specific regions rather than the whole globe.
Why it matters
The ellipsoid is not the same as the geoid, which is the equipotential surface approximating mean sea level. The gap between them — the geoid height — can reach tens of metres and is why GPS-derived ellipsoidal heights differ from orthometric (above-sea-level) elevations. Anyone working with elevation data needs to know which vertical reference applies, or DEM values and contour elevations may be off by a significant offset.
Common pitfall
Treating "datum" and "ellipsoid" as synonyms. An ellipsoid is just the shape; a datum also fixes the ellipsoid's position and orientation relative to the real Earth. NAD83 and WGS 84 use almost identical ellipsoids but are distinct datums, and the difference between them can exceed a metre — enough to matter for survey-grade work.