You will frequently hear it in transportation hubs, such as A következő állomás... ("The next station is...").
While "jövő" is often used for broad future units (like jövő héten for "next week"), "következő" is specifically used when the "next" period is relative to a previously mentioned point in time, similar to "the following week" in English.
The term is neutral and used everywhere from casual chat to professional meetings (e.g., A következő ülésen... — "At the next meeting..."). Distinction from Similar Terms