。
The moment she saw me, she burst into tears.
Literal
She [topic-は] my figure [object-を] see [as-soon-as-とすぐに] cry-burst-out.
私の姿 ('my figure / form / appearance') is a common way to refer to oneself as a sight rather than as a person — 'the sight of me.' Using 姿 instead of just 私 emphasizes that what triggered the reaction was visual recognition. ~とすぐに combines the temporal-conditional と ('when') with すぐに ('immediately'), tightening the sequence to 'the very moment that.' 泣き出す is a compound of 泣く (cry) + 出す ('start out / put out'); the ~出す suffix signals the sudden onset of an action, here 'burst into tears.' Together these elements paint a sharply emotional, almost cinematic moment.