Ellipsoid
The global shape of the earth or a local part of it is described with a datum. A datum defines an ellipsoid plus an offset vector to determine the elevation of the sea level surface.
The ellipsoid is defined by the semi-major axis $r_{major}$, the semi-minor axis $r_{minor}$, the flattening of the ellipsoid $f=1-\frac{r_{minor}}{r_{major}}$ and the eccentricity of the ellipsoid $e^2=2f-f^2$.
The axis of the standard WGS84 ellipsoid, used to describe the global shape of the earth, are $r_{major}=6378137.0m$ and $r_{minor}=6356752.314245m$. This yields a flattening of the WGS84 ellipsoid of $f^{-1}=298.25722356$.
The offset vector is zero for the WGS84 datum, but in general it is non-zero for other datums. The absence of an offset vector simplifies transformations between different CRS, so that a transformation usually implies a first step, the so called datum shift, converting a geospatial position specified with an arbitrary datum to the WGS84 datum, a second step, performing the corresponding CRS transformation and an optional third step, converting back to the original datum.