The origin of the grow and show concept was so that a new breeder could show how his bloodline developed over time by using the hobbyist ponds as his test platform. It could also be used by a dealer that wants to promote a breeders stock that he now sells.
The breeder usually picked a couple of equal quality fish from the same spawning and then sold or gave them to hobbyists that have similar sized systems. These grow and shows could run for years. So this was a way for a breeder to create a name for himself by showing his bloodline traits as being consistent. The hobbyists would then post photos of their koi at pre determined times to be compared and evaluated. Some bloodlines develop sumi in sanke and showa at different ages and peak at different times the show and grow is used to identify that but nowa days is more of a competition between hobbyists to see who can grow the koi the quickest while maintaining the quality...Who can hit that 80cm mark first...usually takes 4-5 years apparently.
Grow and shows are also used to compare koi growth in different water conditions. Koi from same spanwining and placed in hard water and soft water and watch the delopment over time. Theres was actually such a show and grow in the UK a couple of years ago. Read about it here
What is important is that all the koi in the grow and show are the same variety and similar size from the same breeder. There might be a prize at the end for the winner or there might not be one. Its also very important that the rules and terms are defined before the grow and show starts and that the koi variety and origin is made public before people take part.