。
She came here to see me.
Literal
She [topic-は] me [to-に] meet [in order to-ために] here [to-に] came.
The purposive ~ために ('in order to') is the standard way to mark a deliberate goal. It attaches to a dictionary-form verb (会う) and the resulting phrase modifies the main verb (きた). A more compact alternative is the masu-stem + に + motion-verb pattern (会いに行く 'go to meet'), which gives essentially the same meaning. ~ために is more formal and explicit; the stem+に form is the everyday casual choice. Both are correct.