A trombe wall is a type of wall designed to act as a solar thermal collector. The original trombe walls were simply thick walls (to provide a thermal mass) fronted with a piece of glass to trap solar radiation. Modern trombe walls have air vents that help warm air circulate, heating the area behind the wall (generally the interior of a house) more effectively.
The first trombe wall was patented in 1881 by Edward Morse; his first wall was actually just a slab of slate placed in front of an existing window. They were not put into general use until reintroduced by the French engineer Felix Trombe in 1964. Trombe worked with the architect Jacques Michel to build a house heated by passive solar power. While the design did not take the world by storm, it at least put the idea into the public eye.
The trombe wall is an improvement on the basic design of high thermal mass walls. Building materials such as cob and adobe have long had the benefit of being good insulators. The thickness and materials of the walls both keep the sun's heat from warming the interior of the building too quickly during the day, and hold heat to radiate out when the sun sets. Today trombe walls may be made with stone, cob, adobe, metal, or water tanks used as a thermal mass.
The air between the glass and the wall can get quite hot; the most effective way to actively heat your house is to design your wall with air vents at the top and bottom of the inter-glass spaces, allowing heat to flow into your house. As the air within the space heats, it rises up though the vent at the top, drawing cold air up from the bottom, which is heated in its turn.
This same process could work in reverse during the night (as even double-paned glass loses heat much more quickly than does a wall), so trombe walls are often fitted with one-way flaps on the lower vents, so that the air flow cannot go in reverse. They may also be filled with some form of insulation, reducing the amount of heat lost at night at the expense of daytime heat gain.
Trombe walls are generally placed so that they get lots of sun in the winter, but not too much in the summer. This means placing them on the south side of the house, with overhanging eaves to block summer sun. They may also be covered in the summer, or have upper vents that can be opened to the exterior, putting heat back out into the big blue room. Walls are often painted a dark color to increase the amount of heat produced.
As the green movement gains in popularity, trombe walls are starting to gain some popularity. They have the advantage of being highly adjustable to a person's income -- you can fit a trombe system with a thermostat to automatically open and close flaps and shutters, or you can build a simple wall on your own, and adjust it manually. While they can be a great help in reducing energy bills, many locations do not have enough winter sun to heat a house comfortably without some other heat source.
References:
http://www.rahus.org/pdfs/SSH2007Calendar_v8b.pdf
http://en.wikipedia.org/wiki/Trombe_wall
http://www.allanstime.com/SolarHome/Trombe_Wall/index.html
http://www.daviddarling.info/encyclopedia/T/AE_trombe_wall.html