A motion of a Euclidean space is the same as its isometry: it leaves the distance between any two points unchanged after the transformation. But a (proper) rotation also has to preserve the orientation structure. The "improper rotation" term refers to isometries that reverse (flip) the orientation. In the language of group theory the distinction is expressed as "direct" vs "indirect" isometries in the Euclidean group, where the former comprise the identity component. Any direct Euclidean motion can be represented as a composition of a rotation about the fixed point and a translation.