Instead of viewing a box straight on, as in one-point perspective, we are viewing it at an angle. Two-point perspective describes objects that are oblique, or turned at an angle to the picture plane. No planes of the cube or cube-like form are parallel to the picture plane.
In one-point perspective, the height and width of the object are parallel to the picture plane. In two-point perspective, the height only is parallel to the picture plane. Verticals all remain parallel to the vertical edges of the picture plane, but the two sides of the box lead to two vanishing points, one on the right and one on the left.
The vanishing point for one-point perspective is located in the picture plane because parallel edges in the subject are angling sharply away from the picture plane. The vanishing points for two-point perspective are often located some distance away from the drawing, out of the picture plane, to the left and right because the two sets of parallel edges in the subject are angling slightly away from the picture plane.
The location of the vanishing point left (VPL) or the vanishing point right (VPR) for any given set of parallel edges of the subject depends on two factors.
One, the angle between the edges in the subject and picture plane. The closer the edges are to being parallel to the picture plane, the farther away to the left or right the vanishing point (VP) for those edges will be. If the edges of the subject seem to be parallel to the picture plane and not converged in the drawing, it is because the VP for the edges is, in effect, an infinite distance away.
Two, the distance between the observer and the subject. The closer you are to the subject, the closer the VP's are going to be to the center of the subject in the drawing. The farther away you are from the subject, the farther away and the farther apart are its vanishing points in your drawing.
