My parents saw me off at the airport.

Literal

Parents [topic-は] airport [up-to-まで] me [object-を] saw-off [for-me-てくれた].

見送る (to see someone off) is a compound verb: 見 (see) + 送る (send). てくれた marks this as done for the speaker's benefit — the parents' kindness in coming all the way to the airport. まで (up to/as far as) emphasizes the distance.