H0 is a model railroad scale. Pronounced H Oh, the second character is actually a zero, so you're supposed to write H0, not HO or Ho.
0 scale trains are 45 times smaller than their prototype. H0 trains are about half that size, so the real thing is 87.5 times larger. The H in H0 probably stands for 'half'.
Popular manufacturers of H0 scale trains (in Europe) are Fleischmann, Märklin, Roco. The engines run on tracks made by the same manufacturers, but there are also other track manufacturers, like Peco. Or you can build the tracks yourself.
The engines run on electrical power. For historical reasons, you can't run Märklin trains on, ehhm, any other manufacturers electrical system, because they use a centre rail to distribute the power. Also, the engines run on AC as opposed to DC which the others use. Nowadays a lot of trains are equipped with digital receivers which allows you to control a lot of trains at the same time. In the US, the most common system is DCC, which stands for Digital Command & Control. In Europe, DCC is starting to get more common but a lot of people still use Märklin Digital, which is easier (and cheaper) to build yourself, EDiTS and Selectrix.