When baby birds fledge, they grow feathers that are big enough for flying. Just after they fledge, birds take their first practice flights.
You can use the verb fledge in several ways — first, to describe what happens when a bird's feathers grow in. A mother bird — or human — who cares for and raises a young bird can also be said to fledge it. You can also talk about the process of putting feathers on something, especially a hunting arrow, this way: "Once you fledge the arrow, you can use it with your bow." The Old English root word is flycge, "having feathers, or fit to fly."