Alot depends on the species of fish - and there is considerable variation even within families - example, Angelfish:
Put a french angel in a 120 gal tank, feed it well..... it will grow, and grow, and grow.....
Put an emporer in the same tank, fed well...... it will grow, but probably do so quite slowly and end up stunted.
Why is this so? I don't know!
Generally however, I feel it is primarily a combination of 3 things:
Psycological happiness - i.e. environment: Tank mates, tank size, correct lighting and flow, correct aquascaping etc.
Diet - correct type, ammount, and frequency - overfeeding is not always good - it is believed to be the main cause of premature death in lionfish for example.
Water Quality - I believe that there are two elements to water quality - those that we can measure i.e. nitrate, pH, etc. and those that we cannot measure - things such as hormones and enzimes that may be realeased by fish - either OR both can inhibit a fishes ability to grow.
When you get the ballance of these three thing right, your fish will grow quickly and be healthy....... however if deprived of any one of these, it will inhibit growth - to a varying degree depending on how senstive the individual species is, or how severe the "inadequacy" is.
Just my opinions & thoughts - some based on fact - some based on basic undertanding of chemistry & biologogy, and some just my gut feeling & thoughts....
If you care to be more specific about what species you are talking, in what context, and for what reason you ask, we might be able to be more specific.
HTH
Matt