。
She came to see me.
Literal
She [topic-は] me [to-に] meet-[for-に] came.
The bare-bones masu-stem + に + motion-verb pattern: 会いに来た = 'came to meet (me).' The に here is purposive, attaching directly to the verb stem — distinct from the dative に earlier in the sentence (私に, 'to me'). Two different uses of に in the same sentence, doing entirely different jobs — a common point of confusion that learners tend to clear once they learn to recognize the verb-stem+に pattern as a unit.