coplanar points
Lay several coins flat on a tabletop and they all share the surface of the table. Lift one and hold it in the air, and that coin is no longer on the same flat surface as the rest. Points that all lie in one flat surface — one plane — are called coplanar.
Formally, a set of points is coplanar if a single plane contains them all. Any three points are coplanar — even three collinear ones — because three points can always be fitted into some plane (three non-collinear points fit exactly one). The first real test arrives with four points: four points are coplanar only if the fourth happens to lie in the plane fixed by the first three non-collinear ones. Four points that are not coplanar are the corners of a genuine three-dimensional shape, the simplest being a tetrahedron.
Coplanarity is the two-dimensional cousin of collinearity. Lines, too, can be coplanar (both lying in one plane) or not: two lines in space that are neither parallel nor intersecting are called skew, and skew lines are never coplanar. Knowing whether points or lines are coplanar tells you whether you are still doing flat 'plane geometry' or have stepped up into 'solid geometry', where a single plane no longer holds the whole figure.
The four corners of a sheet of paper are coplanar — they share the surface of the page. Lift one corner so the sheet curls, and those four corners are no longer coplanar; they now span a piece of three-dimensional space, like three legs of a stool plus a raised fourth point.
Three points are always coplanar; the test begins at four.
Any three points are coplanar (even collinear ones), so coplanarity only becomes a real condition for four or more points or for two lines.