。
She was moved to tears by his words.
Literal
She [topic-は] his [genitive-の] words [at-に] was-moved-and cried.
感動する ('be moved, touched, impressed') is a strong-feeling verb — used for emotional impact from speeches, films, music, kindness. Source of the feeling takes に. The te-form 感動して links cause to effect: '(was) moved, and (then) cried.' Note 泣いた ('cried') is here written in kana as ないた — a stylistic flicker; 泣いた and ないた are pronounced and read identically.