。
She turned her back on me.
Literal
She [topic-は] me [to-に] back [object-を] turned.
背中を向ける ('turn one's back') is the literal physical act, but in Japanese as in English it doubles as a metaphor for rejection or breaking off relations — 'turn one's back on someone.' Without further context, the sentence can be read either way: she physically turned away, or she rejected the speaker emotionally. The に marks the speaker as the target the back is turned toward (or away from). 向ける is the transitive 'direct toward' (paired with intransitive 向く 'face').