Two points are collinear if there exists a line in which they both lie.
Two points are coplanar if there exists a plane in which they both lie.
If you pick any two points, you can always draw a line (and infinitely many planes) passing through them.
So, you need at least three points in order to have points that are coplanar and not collinear. For example, the vertices of any polygon form a set of points that are all coplanar (they all lie on the plane of the polygon), but are not all collinear.
