A miniature railway is a specific type of narrow gauge railway. Miniature railways have extremely narrow gauges (generally 18" and under), are primarily passenger carrying, and as their most common distinguishing feature, the locomotives on such a railway are at least loosely scale models of full size standard gauge locomotives, as opposed to being built to more appropriate proportions - frequently, for example, the cabs of such locomotives are to scale size rather than really being large enough to fit the crewmember, whose head and upper body normally must protrude above the locomotive.
They are primarily tourist attractions, though some were built with at least hopes of more general utility.
Railways with track gauges smaller than 7" or so tend to be excluded from this category. Locomotives to sizes smaller than that generally require the driver or engineer to ride on rather than in the train, generally operate on raised track, and would be considered operating models rather than the halfway house between model and real railway that the miniature railway is.
The United Kingdom can be considered the worldwide home to the concept, but there are a fair number in the United States also. A good number of them operate in amusement parks and theme parks worldwide.
The largest and best known in the world are both in England; the Romney, Hythe and Dymchurch Railway in Kent, and the Ravenglass and Eskdale Railway in Cumbria.