The idea is to produce more natural hormones, which in turn will increase head, color, as well as overall body shape. In nature, the dominant fish always has the biggest head and thats whats being simulated with the mirror trick.
People who leave mirrors hanging in the tank, or keep a mirror on the side all the time arent doing any good. The fish will eventually see it as not a threat. But on the other hand when he sees himself a couple times a week, It could potentially raise his hormones to improve his overall performance.
On another note, If your fish is scared of a mirror, Like most CA/SA would be, your actually doing more harm than good. You are stressing him plus making him feel threatened by him know there is a fish of his size around. Flowerhorns tend to be more confident in approaching rivals. Also too much mirror can stress the fish. Id advise 45min-1hr 4-5 days a week at the max. Works much better with adult fish as well.