WIG stands for Wing in the Ground and WIG-craft designates a class of aircraft/ship hybrids that use the aerodynamic ground effect.
Basic aerodynamic principle
Aircraft pilots noticed increased lift just before touchdown early on in the history of aviation, and research into this was carried out in the 1920s. Subsequently pilots used this to their own advantage, for example WWII pilots found that it enabled them to reduce fuel use when limping back home from battle. This is due to what is known as the ground effect. An extreme simplification of this is that flying very low creates a high pressure air cushion. In the right conditions this can double the lift produced by the wing.
Why anyone should care
The ground effect means that by skimming low you get greatly increased lift. A type of aircraft designed to operate only in such conditions would be able to carry the same payload more efficiently than conventional aircraft (WIG-craft tend to use about 50% less fuel than a plane) and at much greater speed than ships. WIG-craft could also be used to carry greater payloads than aircraft, at high speed. The Russians, for example, built the 550 ton Caspian Sea Monster in 1966, capable of cruising at 500 km/h at an altitude of 10 feet. A Boeing 747 weighs in at around 440 tons.
Design issues
Power
Although once cruising WIGs save power thanks to the ground effect, getting them off the ground requires a lot of power. The Russian-built ekranoplans (and most other projects to date) all operated from the sea which added to liftoff power requirements.
Stability
Stability has been a critical design factor all along the history of WIG-crafts. For an aircraft to remain more or less flat, its center of gravity and center of effort (CE) have to be more or less in the same place, or the aircraft will pitch upwards or downwards or roll. The main problem is that the air pressure distribution around a wing in free flight and a wing in ground effect are quite different, meaning that the CE is in a different place. The end result is that when a WIG-craft leaves ground effect the CE moves and the aircraft wants to suddenly pitch upwards. In extreme cases, especially when combined with sudden gusts of wind or large waves, this can cause the aircraft to flip over. Large horizontal stabilizers are used to compensate for this.
Vertical Stability
For a conventional aircraft, vertical stability isn't a big issue : altitude variations of a few feet are no big deal. On the the other hand, if you're flying a WIG-craft with the ocean or the ground a few feet below you, and the prospect of losing ground effect a few feet above you are going to be very worried about staying at the same altitude.
WIG-craft in real life
Ekranoplans
The Russians are the uncontested masters of large scale WIG designs. From 1961 onwards the Russians had an ambitious program at the Central Hydrofoil Design Bureau, led by Rostislav Alexeiev. They built many large WIG-craft, including the 550 ton Caspian Sea Monster and the 400 ton Lun. A few of these ekranoplan (the Russian word for WIG-craft) entered service in the Russian Navy. The most recent large ekranoplan was the Lun, built in 1987 as a missile launcher. A second one was partially built, but the collapse of the Soviet Union and reduced military funding have all but stopped Russian efforts.
WIG-train
A Japanese project in competition with Maglev type trains aims to use the ground effect to create a high speed train. The vehicle would have retractable wheels for low speed travel. This project would be cheaper, especially from the point of view of infrastructure. In theory it would use as little as one third of the power of a Maglev when operating at 500 km/h.
Smaller craft
A number of smaller WIG-craft have been built, in many different countries. A project is underway in Germany for the design of a 80 passenger fast ferry. Concerns subsist about how high speed craft could mingle with traditional low speed craft.
Sources:
http://aeroweb.lucia.it/~agretch/RAFAQ/WIG.html
http://www.se-technology.com/wig/
http://www.ikarus342000.com/INTRO2.htm
http://www.fas.org/man/dod-101/sys/ship/row/rus/903.htm
http://www.infinity21.co.kr/non-it/wig_homewig_history.html