He bowed his head remorsefully, realizing he had made a huge mistake.

remorsefully 是副词，由名词 remorse（悔恨）加上形容词后缀 -ful（充满...的）变成 remorseful（充满悔恨的），再加上副词后缀 -ly 构成。意思是"懊悔地、悔恨地"，表示带着深深的后悔之情做某事。