She was about to go out.

Literal

She [topic-は] go-out about-to-do-was.

~ようとする pairs the volitional form with する to express imminence — 'about to do.' Add the past progressive ~ていた and you get 'was about to,' which captures a moment caught in the act of starting but not yet complete: she had her shoes on, her hand on the door, but hadn't actually left. This pattern is one of Japanese's preferred ways to talk about an action whose unfolding is interrupted or whose outcome was about to happen but didn't quite — 'I was about to call you when…' — so it often sets the stage for a contrast or a twist of events.