The person directly responsible for the nominal pipe size was a gentleman by the name of Robert Briggs. Briggs was the superintendent of the Pascal Iron Works in Philadelphia. In 1862, he wrote a set of pipe specifications for iron pipe, and passed them around to all of the mills in the area.
Realize that in 1862, this country was engaged in the Civil War. Each pipe mill made its own pipe and fittings to its own specifications. Briggs tried to standardize the sizing, which would also help the war effort. The pipe and fittings would be interchangeable between mills. This was rather novel in 1862.
The pipe standards went on to become known as the “Briggs Standards.” They eventually became the American Standards, and finally the standards used for modern day pipe.
The current ASTM A53 Steel Pipe Standard uses basically the Briggs Standard for pipe sizes 1/2 inch through 4 inch. You will notice that after 4 inches, pipe starts to get closer to the actual dimension used to identify the pipe.
So, you are probably asking, where did the sizes come from? Well, they were the sizes of the dies used in Pascal Iron Works. Briggs made everyone adjust to him. Hence, the name “nominal” pipe size came about, meaning “close to” or “somewhere in the proximity of” the actual dimension.