The horizon is a plane level with the eye line of the viewer/painter/drawer/witness/whatever
(knew that one already! ha!)
The principal vanishing point is a point on the horizon directly opposite the viewer (I'll call them that from now on). A line from the viewer's eyes to the principal vanishing point would be perpendicular to the horizon.
(I knew that one too... I think ^-^)
All lines parallel to the one between the viewer and the principal vanishing point will meet at that point (so long as they are on the plane of the horizon or any other parallel plane). Any other parallel lines on the plane of the horizon or any parallel plane, whichever way they point, so long as they are parallel to each other will meet at the same vanishing point on the horizon line. This point will be where they would otherwise cross that line.
All planes parallel to the horizon will meet at the horizon if allowed to continue... think of a set of shelves.
(I knew that one, definitely!)
Any parallel lines not on the plane of the horizon or a parallel plane will meet at a point directly above or below where they would have met the horizon had they been on that plane (confused yet?). This is easier than it sounds - I tried it out. Just draw a line at right angles to the horizon line then draw a a diagonal line that crosses it - either above or below - if you draw other lines that meet at that point they will appear to all be parallel and all be on the same plane.
Here are some drawings I made on the train trying to get my head around these things:
This is going to be really useful! Why didn't I learn it when I was fifteen! Arrgh!