Dihedral, properly defined as the angle where two planes intersect, has an aeronautical connotation involving flying surfaces (wings, but could also be tail surfaces) where the tips are higher than the roots of the surfaces.

As such, dihedral has the word anhedral for an antonym. Flying surfaces with anhedral have "drooping" tips, or tips lower than the root of the surface. (See the AV-8 Harrier for an example of wing anhedral, and see the Predator UAV and F-4 Phantom for examples of horizontal stabilizer anhedral.)

Interestingly, I have also seen some old textbooks use cathedral as an antonym for dihedral, which certainly invokes a mental picture (for me at least) of the planes of a roof soaring upwards towards the line denoting their intersection.

Wing dihedral is incorporated into an aircraft to help provide lateral stability; i.e., stability about the roll axis. (Anhedral in the AV-8 is present to counteract other stabilizing effects on the aircraft to keep it from being too stable. In the F-4's case, the horizontal stabilizer anhedral adds extra stabilizing force and area about the yaw axis, and in the Predator the stabilizer anhedral allows landing gear wheels to be mounted in the tips of the stabilizer.*)

An earlier writeup in this node attempts to explain why dihedral contributes to lateral stability without, in my view, entirely succeeding.

It's easily enough demonstrated, however, with a 3x5 index card, or any other small oblong rectangular piece of paper.

Fold your card in half about its shorter dimension, and open it back up, almost all the way. Hold it out in front of you so that you see it, edge on, as a shallow 'v'.

You're now looking at your index card as if you were an air molecule, rushing towards the wing's leading edge, (or, equivalently, being rushed by the wing; it makes little difference).

As an air molecule, you and your mates are about to smoothly and rapidly flow above and below the airfoil of the wing. Bernoulli's law will then work its magic and produce lift, just like you learned in school.

However, if your school was as mediocre as mine, it was probably not adequately explained that it's not just the shape of the airfoil that produces lift. The airfoil must be held at a positive angle of attack with respect to the oncoming airflow.

In fact, for most normal regimes of flight, the lift produced by the wing varies just about linearly with angle of attack (meaning simply that if you double the angle of attack, you double the lift).

So, to appreciate this from the air molecule's perspective, you have to tilt your index card so that you don't see it exactly edge-on. Tilt it so that the further edge is lower. You should now see something resembling the following, and, as always in a ring-wraith writeup, forgive the execrable ascii-art:

....                 .... 
 .  ....         ....  .
  .     .... ....     .
    ....    .    ....
        ... . ...
            .

Note that each panel of the wing, having an identical agle of attack relative to the oncoming airstream (your line of sight,) will produce identical lift.

But now let's say our wing encounters some turbulence: a gust of wind, a bump. One wingtip is tilted higher than the other. Simulate this by rotating your index card about the fold so that one side is higher:

                     .
                    .
                  .  .
                .   .
              .   .
.............   .
 .          . .
  ...........

The higher side of the wing now has a lower effective angle of attack, and will produce less lift. The lower wing will produce more, and will therefore tend to rotate (bank or roll) the aircraft back to where both wingtips are level. Don't believe this? Keep rotating your card model, then, until the high side is vertical. Note that it now has a zero angle of attack relative to the airflow - you are seing it exactly edge on.

The stabilizing effect is very effective, and very reassuring to a new pilot; it means that you can let go of the controls and the airplane will right itself. If you take flying lessons, which I hope you do because it's a priceless experience, your instructor may demonstrate that it's possible to use this effect to turn the plane entirely with the rudder, instead of the usual way with ailerons and rudder used together in a coordinated fashion. He or she will do this by pushing and holding a rudder pedal, let's say the right one. The nose of the plane will swing to the right, the left wing will advance and, due to the dihedral, will then have an increased angle of attack. (Try this with your index card and verify that ring_wraith speaks words of truth.) The wing with the increased 'AOA' has more lift, and therefore banks the plane to the right. And, as you learned in lesson one, it's the bank angle that really turns the plane, since it tilts the lift vector to one side, in this case to the right, AKA the inside of the turn. This works quite well, if less 'positively' than a normal bank controlled by the ailerons. It also feels weird and awkward to a pilot (and to passengers) which is why it isn't a normally recommended technique.

There are aircraft designs, however, that depend on the dihedral stability effect. There are any number of ultralight (The Brits know them as microlight) aircraft designs that have no ailerons, but plenty of dihedral with which banks and turns are controlled.

Dihedral is also critical for virtually all types of free-flight model airplanes, as you might imagine. These designs often take dihedral to another extreme: polyhedral wings. In a polyhedral wing design, the wings start out from the center or root at a shallow dihedral angle, and at some point out along the span there is another break from which the wingtips slope upwards at an increased angle.Radio-control model gliders, sailplanes, and trainers also frequently lack ailerons and therefore depend on dihedral. It makes them stable and easy to fly for a new pilot, and also easier to control when they are way, way off and just a speck in the sky.

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*Correction. I just had one of those "what was I thinking?" moments.

A glance at a photo of a predator UAV reminds me that it does not, in fact, use its anhedral stabilizer as mounts for landing gear. It has a quite conventional fixed tricycle landing gear.

Which raises the question, "what were THEY thinking?" I know of no good aerodynamic reason for such a pronounced anhedral in the predator's horizontal stabilizer, and it seems to make the tail surfaces very vulnerable to ground impact damage in an awkward landing...the tips of the stabilizer are no more than a couple of inches above the pavement when the aircraft is parked. So why? Is it a radar signature reduction measure? Are there antennae mounted in the stabilizer that are sensitive to this angle? You got me.