What does “je m’en occupe” mean in French?

Je m’en occupe is how you accept a task: “I’ll handle it, leave it with me.” S’occuper de covers dealing with a problem, a booking or a broken drawer, and it also covers looking after people — elle s’occupe des enfants. The en stands in for whatever was just mentioned, which is why those three words work as a complete answer on their own.

Close by but not interchangeable: être occupé is to be busy, and occupé on a door is “engaged.” Turn s’occuper de on someone else and it goes sharp — occupe-toi de tes affaires is “mind your own business,” delivered with none of the helpfulness of je m’en occupe.