The term is an abbreviation for "Numerical Indicator experimental No.1, in other words, NIX-1", later it has totally melted into the common language and is used that way, even today. The first stable and well-functioning nixie tube construction was invented by Haydu Brothers Laboratories, which was founded by two Hungarian brothers namely George Haydu and Zoltan Haydu in 1936. In 1954 everything, including trademarks, production lines needed for manufacturing (and the inventors themselves) were bought by Burroughs Corp. and that's when mass production started. This is the reason we refer to the Hungarian brothers as the fathers of nixie tubes – but the next steps were taken by the more competent Burroughs Corp.
To be precise, it should be mentioned that tubes with numerical display were already being used in the early 1930's, however the real Nixie tubes started to appear around the early 1950's as the "display" of several gadgets, e.g. military apparels, printing machines, early calculators and instruments, or even the plaquettes of the New York stock market. They could be on the top for only until the middle 70's, when LED-technology took over their place from one day to the other, because of cheaper production, longer lifetime and their use in wider fields. However LEDs are much more developed, they are nowhere near to nixie tubes in terms of aesthetics. Nowadays, one can find countless wonderful products using them, as retro-clocks, thermometers, incubus-lights, and other splendid things are being built by a bunch of dedicated radio-amateurs and crazy designers; they've got the individuality back they fought out in the past, and what they deserve in these grey digital days.
Concerning their setup and function, usually there are 10-12 cathode-threads in electron tubes (that means blown glass) filled with 1% neon-gas that forms digits or different symbols in front of each other, covering the ones in the back a bit. If we give it 120V AC voltage, it will shine in a deep orange colour (in some cases purplish blue), making the digits visible. That's what we call gas-eruption light phenomenon, which is similar in practice to the functioning of an incandescent.
The mainly Russian nixie tubes presented by me are perfect examples of the long forgotten intercontinental space race, and the growth of domestic use of electronics. A wonderful instance for this is the shape of the digits "5" and "2", having the same forms, only upside down. This represents a simple and cost-saving planning philosophy, provided by the superpower of the Cold War.