Dinosaurs were the dominant life form on earth for 170 million years, finally going extinct at the end of the cretaceous period, 65 million years ago, when a huge comet crashed into the Gulf of Mexico. Birds of prey are descended from theropods, a type of dinosaur that walked on its hind legs, while their smaller forelimbs were used, like arms and hands, for reaching and grabbing.
Theropods are usually represented by T-Rex, Allosaurus and Velociraptor, though most theropods were no larger than dogs. During this long period, the earth underwent climate change, just as it does today, and fossilized remains indicate that feathers began to develop about 150 million years ago, and those theropods which developed them survived to breed in cooler temperatures, while those lacking them perished.
Generally speaking, feathers are more effective in maintaining constant body temperature than are the fur of mammals. Birds of prey don’t migrate because they are cold, but rather because much of their prey hibernates, thus severely cutting their food sources.
As with birds of prey today, female theropod dinosaurs were considerably larger than males, and not always safe to approach! The second use of feathers was for colorful and ornate display, to impress a larger female from a safe distance, and also to warn away other males, who may try to woo the same female. Think of how wild turkey toms strut before their females.
The first feathers were symmetrical, meaning that they were not structured to provide the lift required for flight. The evolution of flight was later enabled by mutations, or alterations in genetic material, which changes a feature either to the advantage or disadvantage of the creature affected. In the case of feathers, mutations produced feathers which were asymmetrical, which had the effect of enabling lift to smaller, predator-fleeing or prey-chasing theropods. Picture how flying fish escape their predators by gliding away, or how flying squirrels glide from higher to lower branches.
The asymmetrical feather was one of those mutations which conveyed a survival benefit. Those who possessed them were less likely to be caught by predators and more likely to help them provide for their own sustenance. As a result, these lucky theropods, and later early birds like Archaeopteryx, were more likely to survive, mate, and have offspring. To these offspring they would pass along the gene for asymmetrical feathers.
Illustration of Arcaeopteryx courtesy wiki commons.