Feathers are something like the fur of birds. They decorate themselves with them to impress other birds with their colorful feathers.
Just like the peacock likes to do. Air is trapped between their feathers and their skin. It keeps the bird's body warm. Just like a down jacket keeps you warm. There are feathers in it, too. In addition, the feathers are waterproof. So birds can swim without getting their skin wet.
Some birds also camouflage themselves with their feathers. Their feathers then have the color of their surroundings. This makes them less easily recognized by enemies. If birds had fur, they would not be able to fly. Only with their feathers on their wings can they soar into the air. These feathers lie close and smooth together. Like a zipper, they interlock and overlap. This creates a wing like that of an airplane. The springs are soft and pliable, yet quite firm. A steel feather as large and thick as a bird's feather would break much more easily.
in a nutshell: birds have feathers for decoration, protection, camouflage and of course to fly.