What is it?
The E6B flight computer (or just E6B) is a mechanical computer (slide rule device) designed to quickly and easily perform a number of calculations which are relevant to aviation. Although nearly all modern aircraft have electronic flight computers, and pilots can purchase inexpensive electronic versions, knowing how to use an E6B is still useful as it never needs batteries, is extremely difficult to break, and is flat enough to be tucked into any flight bag as an emergency backup. Plus, they won't let you bring electronic flight computers into the FAA Private Pilot written exam - so you'd better get used to it if you're planning on becoming a pilot.
What does it look like?
It has two main components. The first is a two-piece circular slide rule which does multiplication and division calculations. The front of this unit has two discs, one fixed and one smaller one which rotates; the edges of these discs are marked with numerical scales and with particular constants. By aligning the 'constant' points on the inner and outer discs (for example, 'gallons' and 'hours') you can perform calculations using those two values (gallons per hour of fuel burn) by matching inner and outer wheel markings. It can convert kilometers to miles, pounds to kilograms, fuel burn to time, airspeed to distance, and so forth. Instructions are printed on the front surface, although if you're not familiar with slide rules in general or the E6B in particular they are somewhat opaque.
On the other side, there is a clear plastic surface which is contained within another inner disc and can spin. The second component of the computer, a flat plane with precalculated wind arcs on it, fits through the circular computer so that the arcs can be seen through the clear plastic. This side is used for calculating wind correction angles as well as ground speed corrected for winds.
Where did it come from?
The history of the E6B is fairly complicated. Various sources agree that a Cornell University graduate named Philip Dalton, who became an artillery officer (and thus was intimately familiar with the military use of slide rules) invented a simple aviation computer in the early 1930s. He iterated it through various versions, with the 1933 Model B being the first popular one. That model was basically the 'front' circular computer. He added functions to it, putting a double-drift diagram on the back in 1936. The U.S. Army Air Corps bought that one and designated it the 'E-1A' (with /B and /C variants). Dalton continued to tinker, producing a more complex device for burgeoning commercial aviation, ending up with a relatively complex tool with a 'continuous loop' belt inside for performing drift calculations. The military thought that was too fragile, and he modified it again into a two-piece, flat slide rule device and named that the Model H. The Army took that one and designated it the E-6A. At the further intervention of the Air Corps, he made some tweaks and renamed it the Model J; the military version became the E-6B.
After that, the Pearl Harbor raid caused the U.S. military to begin ramping up significantly, and over 400,000 Model E-6Bs were ordered. Although Dalton continued to tweak the device up until his death a few years later, military users (navigators and pilots) who joined in the huge build up just prior to and during World War II came to know it as the E-6B - and even though its designation continued to change inside the military as small changes were made, the users continued to refer to it as the "E-6B".
After Dalton was killed while training a student pilot, the Weems company continued to try to update the device for the civilian market and tried various names - but the thousands of veteran pilots, many now flying in civil aviation, continued to refer to the device by its familiar name and the 'E-6B' and 'E6-B' and other subtle variants were all used by various marketers. The E6B is now a relatively standard device and available from a number of manufacturers. ASA and Jeppesen both make a metal version sold in most U.S. pilot shops for under $20.
The E6B is such an iconic bit of flight gear that Commander Spock can be seen using one in two episodes of Star Trek: The Original Series (although I'm sure that his probably had Warp Factors scribed on it somewhere; I can't see him caring about gallons of avgas burned per hour or the ground speed for a 20-kt wind correction!)
(The history information was originally taken from a post by Kevin Darling on the airtalk boards, augmented and checked with several other web sources).
For a quick tutorial on the use of the E6B as well as to see what it looks like, see the Online Flight Training channel on YouTube, which has an E6B tutorial playlist!
(IN 5 9/30)