ichidan verb
become famous; make a name for oneself
Used when someone gains recognition or success, often in a field like arts, business, or academia.
彼は若くして小説家として世に出た。
He became famous as a novelist at a young age.
ichidan verb
go out into the world; make one's way; appear; be published
Broader sense: to enter public life, to be released or published, or to appear in society. Often used for books, works, or people starting a career.
彼の新作がついに世に出た。
His new work has finally been published.
大学を卒業して、いよいよ世に出る時が来た。
After graduating from university, the time has finally come to go out into the world.