I'll piggy back on this to supplement the evolutionary reasons for this.

Mammals, birds, and fish all use sexual selection as a primary basis for their reproductive process. Demonstrating you are an exceptional member of your species is vital to attracting a mate and reproducing successfully. Typically, a Male of a species competes with others for the attentions of the choosy female. To do so they must prove they are stronger, faster, smarter, better fed, and generally more capable of supporting and/or protecting the dependent female than their competitors, or at the very least that his genes are worth the significant female energy investment to bearing offspring.

In the mammalian world, these competitions are best done in a way that is synergistic with survival demands. What better way to prove you can survive better than an opponent than to overcome them in some physical contest: Fight, be bigger, thump louder, etc. often while demonstrating a handicap that accentuates your ability to overcome (think Ginormous antlers that take a lot of food and energy to make and whose weight alone is a hinderance)? Even if you lose this contest you'll survive, learn from the experience, and the innate toughness it required in the first place makes you better to survive in the wild generally speaking.

Birds cannot tolerate the physical stresses of violent competition because the physics they rely on do not allow their skeletons to support it. It would be way to easy for hollow bird bones to break turning a fight lethal 90% of the time. How to compete then? For them, physical indicators are better: bright colourful pigmentation is energy intensive to produce. It will fade if the male is malnourished. It also reveals the presence of disease or parasites. The disadvantage of being so visible proves you are cunning as you're still alive despite it. Coupled with other attributes and performances this allows males to compete with Displays instead of fighting, for a much more survivable experience.

The reasons behind Fish colouration are less clear afaik. Best guesses are that the particular colour pattern of a fish allows them to camouflage in their colourful environment better.