The children discussed their upcoming holiday animatedly, waving their hands with excitement.

animatedly 是副词，由形容词 animated 加副词后缀 -ly 构成。animated 来自动词 animate（使有生气、使活跃），表示"活跃的、兴奋的"。 animatedly 描述的是讨论时的状态，意思是"兴奋地、活跃地"，强调孩子们讨论时充满活力和热情的样子。