She asked me to meet her at the station.

Literal

She [topic-は] me [to-に] station [at-で] meet-(arriving) [as-ように] asked.

出迎える ('to go out to meet someone arriving') is a more specific verb than plain 迎える: it focuses on physically going out to greet a person on arrival — meeting at the airport, picking someone up at the station. Common in formal hospitality and travel contexts. The polite past 頼みました (rather than casual 頼んだ) shifts the register a notch — perhaps the speaker is reporting to someone they'd address politely.