Think of a hen on a nest. She has settled onto her eggs and she is not getting up — not for food, not for you. She is silent, up, turned inward, and she will peck the hand that comes near. Every use of broody can be seen growing out of that one bird. Sit on your own thoughts the way she sits on her eggs, and you are broody in the quiet, closed-off sense. Feel that same protective pull toward a baby of your own, and you are broody in the other. Even a low grey sky can look as if it is sitting on something it will not show you.
From the word’s history
Wiktionary traces broody to Old English brōdiġ, formed from brood plus -y, with German brütig as a cousin. A brood is a sitting of eggs or the young that come from it, so the bird sense is the oldest layer and the human senses sit on top of it.
Wiktionary 把 broody 追到古英語的 brōdiġ，是 brood（一窩雛鳥／孵蛋）加上 -y，德語的 brütig 是它的表親。brood 本來就是「一窩蛋或雛鳥」，所以鳥的意思是最底下那一層，講人的用法都疊在上面。
Wiktionary, "broody"
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