When you do something eagerly, you're not dragging your feet or waiting to be asked twice. You're leaning forward, ready to go.

A dog waits eagerly by the door when it hears the leash jingle. Students eagerly raise their hands when they know the answer. You might eagerly tear open a birthday present or eagerly agree to a trip to your favorite restaurant.

Compare it to enthusiastically, which emphasizes energy and spirit, while eagerly emphasizes that hungry, can't-wait feeling of anticipation.