。
Even though she was busy, she came to see me.
Literal
Busy-was [despite-のに] she [topic-は] me [to-に] meet [purpose-に] came.
のに ('although, even though') marks contrast between expectation and reality — busy people normally wouldn't come, yet she did. Distinct from だろうに ('she must have been busy'), where the speaker is conjecturing rather than stating known fact. The 会いに来た construction stacks the purpose marker に onto the verb stem 会い + the motion verb 来る — a tight 'come in order to meet' frame.