Ray, sorry we all apparently missed this question (you just *had* to ask the day after Christmas, huh?...lol). Amino acids are comprised of proteins and act in corals similar to the way they act in people. For example, some corals have (and others are missing) a particular type of amino acid that basically acts as a "sunscreen" to protect themselves against UV radiation. Other amino acids are a food source for symbiotic bacteria in some corals.
Scientists don't know the exact requirements of each type of amino acids or how much aquatic life needs (carnivores require a diet higher in amino acids than herbivores though).
Part of the BluCoral feeding method (which is what I lazily do) is a high-protein => high nutrient environment. About an hour before the lights go off, I'll dose amino acids. This puts the corals almost into a "feeding frenzy". The polyps will extend further out, which will help them take in more food when fed (keep in mind though, that most corals get about 95% of their food from light though.) An hour after dosing the amino acids, I'll add in the food I specially make for them. The corals can take in as much food as they possibly can in this time (hence the high nutrient environment). This gives corals a more vibrant bright color (as opposed to the low-nutrient systems like Zeovit or Prodibio that give a pastel-color to the corals.) To prevent algae, there needs to be a good nutrient export system (like an oversized skimmer, etc.)
Right now, amino acids are just one of those things that some people get great results with...so they use it. Other people don't use it...still get great results though. There isn't enough research on it to be honest. I consider it just a food source...and one more bit of variety of food can't hurt IMO.
*shrug*