This demonstration contains four examples of how a Clay SOP is used. The points have been animated to better visualize this.
Matrix - Point transformation is given by a matrix.
Vector - Point is translated along a vector.
Point - Point is moved to an absolute XYZ position in object space.
Primitive - Point snaps to the (U,V) of the primitive in the 2nd input of to a (U,V) on itself if no 2nd input is present.