To set out on a journey; to leave one's current place to travel. Can be used literally or figuratively (e.g., embarking on a new phase of life).
今週末、久しぶりに旅に出る予定だ。
I'm planning to set out on a trip this weekend for the first time in a while.
仕事を辞めて世界一周の旅に出た友人がいる。
I have a friend who quit their job and set out to travel around the world.
小説の主人公は悩みを抱えて旅に出る。
The novel's protagonist leaves on a journey burdened with worries.