This is by far the most popular scale today, world-wide. It dominates the hobby by a very wide margin, its four major advantages being the great variety of available ready-to-run and kit equipment, ease of handling by youngsters, its economy of space, and a physically comfortable miniature scale to work with.
HO stands for Half O Gauge. O Gauge today has a track width of 32mm, with a scale of 1:48 (North America). HO today has a track width of 16.5mm, with a 1:87 scale (North America).
You may have seen references to OO Gauge. OO is the equivalent of HO in the UK, with the same track width of 16.5mm, but with a scale of 1:76, with the result that the track width is slightly under-scale. (Precision UK prototype modellers therefore prefer the EM [Eighteen Millimetre] gauge.)
HO/OO scale and gauge is a direct linear descendant of the larger trains of the original toy train era. That era is generally accepted as having begun at the Leipzig (Germany) trade fair in 1891, where the German firm of Märklin Brothers defined the original toy train gauges 5 (120 mm), 4 (75mm) , 3 (67mm), 2 (54 mm) and 1 (45mm). Gauge O appeared around 1900. The steady miniaturization of the hobby scales and gauges was driven by the spread of the toy trains' popularity from a simple circle around a Christmas tree, to a new kind of toy for the children of the well-to-do who had large homes; and then to the population at large, whose financial and space resources were generally rather more limited.
Thus it was that the first OO "table top" Gauge trains produced by the German firm of Bing first appeared in 1922, followed by Märklin's trains in that scale in 1935, and by the popular UK maker Hornby in 1938.
World War II interrupted the further development of trains in this scale.
It was in the 1950s that the toy train era finally gave way to model railroading as an adult hobby. This transition was stimulated by prosperity, improved miniaturization of electric motors, and the appearance of electronic applications. Arguably, the two most significant transformations in the 1950s era towards prototypical resemblance were the replacement of tin by plastic as a manufacturing raw material, and the move from three-rail to two-rail electrification. Add to that improved manufacturing and detailing capability, and the model railway industry was born. The traditional larger scales faded into the background, manufacturers reconfigured themselves as the industry changed direction, acquiring and/or re-working traditional brand names, and the thrust of the hobby was now in the direction of closer adherence to the prototype in its detailing. The modelling community now aspired to building something that looked like a real railroad in miniature. Today, the HO modeller's choices are almost limitless in the areas of locomotive and rollingstock ("equipment") selection, layout design, and electric and electronic methods of control. The basic options are RTR (ready-to-run/operate) locomotives, rollingstock, powerpacks, scenery), kits (assembly of commercially-prepared parts of equipment and scenery), or scratchbuilding (the building of a model railway by hand from a minimum selection of commercially-available parts).
Most modellers start with ready-to-run equipment, and graduate to kitbuilding in areas that interest them. Some modellers develop the necessary patience for handbuilding track, which has advantages of appearance, low cost, and the ability to create track formations ("special work") not commercially available.
As with all endeavours, it pays to start simply, with a modest layout ambition, but with an investment in good locomotives, track and power applications. Few of good quality is much better than plentiful but of poor quality. Most modellers are into the hobby for their lifetime, and it pays to invest in good quality.
Many modellers prefer to work on their own. Others may want the social contact of a club. All modellers are helped by information about their hobby. There are many good "how-to" books available from hobby stores. A subscription to a model railway magazine is a good idea. There is a lot of information on the internet today, but some of the best immediate advice comes from others in the hobby and from a knowledgeable local hobby dealer. Hobbyists at a model train show tend to look busy as they concentrate on operating their trains, but stop someone to ask questions, and chances are that you will be well-rewarded. HO scale is a good starter choice in the hobby, and as their interests progress, many modellers come to "dabble" in another scale, or develop an interest in narrow gauge modelling.
And by all means be sure to have the complete set of these leaflets.