A U-bolt is a bolt in the shape of the letter U with screw threads on both ends. U-bolts have primarily been used to support pipework, pipes through which fluids and gasses pass. As such, U-bolts were measured using pipe-work engineering speak. A U-bolt would be described by the size of pipe it was supporting. U-bolts are also used to hold ropes together.
The nominal bore of a pipe is actually a measurement of the inside diameter of the pipe. Engineers are interested in this because they design a pipe by the amount of fluid / gas it can transport. As U-bolts are now being used by a much wider audience to clamp any kind of tubing / round bar, then a more convenient measurement system needs to be used.