。
She went outside to look for a taxi.
Literal
She [topic-は] taxi [object-を] look-for [for-に] outside [to-へ] went-out.
The pattern [verb stem]+に+[motion verb] expresses purpose of motion: 探す ('look for') becomes the masu-stem 探し, then +に gives 'in order to look for.' This stem-に frame is one of the cleanest ways to attach a goal to a movement — 食べに行く ('go to eat'), 買いに来る ('come to buy'), 見に出かける ('go out to see'). Pairing it with 外へでる ('go outside') gives a small directional drama: she stepped out and started scanning for cabs. Notice 出ました is written でました in kana — informal-feeling even though the verb form itself is polite ます.