。
She was so moved that she shed tears.
Literal
She [topic-は] moved [so-て] tears [object-を] flowed.
感動する ('to be moved emotionally') is the everyday verb for being touched by something — moved by a film, a kindness, a performance. The te-form 感動して here links cause and result: 'being moved, [so] tears flowed.' 涙を流す ('to shed tears') is a set phrase using the transitive 流す ('to make flow / pour out') — note that even though tears flow on their own physically, Japanese frames it transitively, with the person doing the 'flowing' of the tears. The intransitive equivalent 涙が流れる ('tears flow') exists too, and shifts the framing to make tears the agent. The transitive choice here puts subjective ownership on the moment.