Though the nut and bolt concept has apparently been around since the 16th century or earlier, in the early 19th century the process was usually done by local blacksmiths. The New York company soon found a niche making and selling standard stove bolts and this led to becoming leaders in nut and bolt systems. The company invented and developed machinery to make nuts and bolts efficiently and soon were selling their products nationally.
I'm curious about their role in standardizing pitch and thread forms, as about that time, Joseph Whitworth in England and William Sellers in the USA were both proposing standard thread systems and there doesn't seem to be any mention of RB&W at all.
In any case, Russell, Burdsall & Ward grew and in the early 20th century they started concentrating on fasteners for the growing automotive industry. That prompted a move to Ohio and in 1973 the old Port Chester, New York plant was closed.
In 1995 the company was acquired by Park-Ohio Industries and is still in business today, with factories around the world, including a sizeable Canadian operation in Mississauga, Ontario.
More on the Canadian connection here.
Company history here.