。
She came up to me.
Literal
She [topic-は] me [to-に] approached [toward me-てきた].
近づく ('to approach, to come/get near') is the intransitive verb meaning 'to get close.' Pairing it with the auxiliary ~てくる adds the directional flavor: the approach was directed toward the speaker. Without ~てくる, 彼女は私に近づいた would be neutral; with ~てくる, the speaker is at the center, and she's moving inward into their space. The combination 近づいてくる is one of the most natural-sounding ways to describe someone approaching you in a narrative.