HO or H0 is the most popular scale of model railway in the world.
According to the NMRA standard S-1.2 predominantly used in North America, in HO scale, 3.5 mm (0.1378 in) represents 1 real foot (304.8 mm); this ratio works out to about 1:87.1. According to the MOROP standard NEM 010 predominantly used in Europe, the scale is exactly 1:87.
In HO, rails are usually spaced 16.5 mm (0.64961 in) apart which models the standard railroad gauge of 1,435 mm (4 ft 8 1?2 in).
The name HO is derived from the fact that its 1:87 scale is approximately half that of O scale which was the smallest of the series of older and larger 0, 1, 2 and 3 scales introduced by Märklin around 1900. In most English-speaking markets it is pronounced "aitch-oh" and written with the letters HO today, but in German it is pronounced "hah-null", and still written with the letter H and numeral 0.
Modern HO trains run on two-rail track, which is powered by direct current (varying the voltage applied to the rails to change the speed, and polarity to change direction), or by digital command control (sending digital commands to a decoder in each locomotive). Some trains, most notably by Märklin of Germany, run on alternating current, supplied by a "third rail" consisting of small bumps on each tie down the centre of the track.
On simple, usually temporary layouts, power is supplied by a power pack consisting of a transformer and rectifier, a rheostat or potentiometer for regulating voltage supplied to the track (and thus train speed), and a switch to control train direction—a double pole, double throw slide or toggle switch wired to reverse the polarity on the rails. On permanent layouts, multiple power supplies are traditionally used, with the trackage divided into electrically isolated sections called blocks; toggle or rotary switches (sometimes relays) are used to select which power supply controls the train in a particular block. With the advent of digital command control, block divisions are largely eliminated, as the computerized controllers can control any train anywhere on the track at any time, with minor limitations.
For more history, visit Wikipedia.
What's it worth? Take a look at this H0 price guide: sold listings for a value indication.