A size of toy or model electric train. O is the size, and gauge refers to the distance between the outer rails. The gauge of the O train is 1 and 1/4 inches. The most prolific maker was Lionel. O gauge also refers to the basic curve of Lionel trains, that being 31 inches in diameter.
We have an O gauge model railway in the basement.
Lionel makes O Gauge, which is larger than H.O.