Terminology
H0 originally meant "half-zero," as in half the size of a 0-gauge train. The name is correctly spelled with a zero although it is commonly spelled with the letter O (i.e. "HO").
Definition
An H0 model train is a train crafted to approximately 1:87 scale, or approximately one real foot per tenth of an inch of model size.
Origin
H0 model trains were introduced in Europe in the 1930s by German manufacturers looking to compete against the similarly-sized 00 scale model trains.
History
H0-scale trains became popular in the 1950s, due in part to the rise of model railroading as a hobby. The small size allowed for easier, more elaborate modeling and layout.
Fun Fact
H0's 1:87 scale is popular with model hobbyists of all stripes, including those who build model trains, planes, automobiles and military craft.