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She's out on an errand.
Literal
She [topic-は] errand [for-で] out-of-office-currently is.
外出中 stitches together 外出 ('going out, leaving') + the suffix ~中 ('during, in the middle of'), forming 'currently out / not at one's place.' The suffix ~中 is hugely productive: 食事中 ('during a meal'), 仕事中 ('at work'), 会議中 ('in a meeting'), 通話中 ('on a call'). It commonly appears on workplace status messages, away signs, and 'do not disturb' notices. 用事 captures any sort of personal business — errand, task, appointment — without specifying its nature. The で marks the reason or purpose of being out.