Objects are coplanar if they lie in the same plane. We typically think of these objects as points or lines, or 2D shapes. Points, lines, or shapes are non-coplanar if they do not lie in the same plane.
Collinear points lie on the same line. If points are collinear, they are also coplanar. However, coplanar points are not necessarily collinear.
In the diagram above, points A, B, and C are collinear and lie in plane M so, they are collinear and coplanar (you can draw infinitely many planes containing line AB). Points A, B, C, and D lie in plane M so are coplanar but not collinear since they do not lie on the same line.
Point F does not lie on plane M so it cannot lie on line AB. Therefore, it is neither coplanar to M nor collinear with A, B, and C.
The x- and y-axis are coplanar since they form the Cartesian coordinate plane.
In the diagram above, AD intersects parallel planes M and N at points A and D. Points A, B, C are in plane M and points D, E, F, G, and H lie in plane N so, they are non-coplanar. Lines EF and GH lie in plane N so they are coplanar. Lines EF, GH, and AD do not lie in the same plane so they are non-coplanar.
The rectangular prism below has vertices at A, B, C, D, E, F, G, and H.
The vertices A, B, C, and D on the front face are coplanar but not collinear. This is true for each of the 6 faces that make up the prism.