Definition
When a responsibility or decision lies with someone, they bear the responsibility for it.
由（某人）負責
The final decision was authorized to the manager, so all responsibility rests with him.
最終的決定權在經理，因此所有的責任都由他承擔。
The success or failure of this project ultimately rests with you.
這個專案的成功或失敗最終由你負責。
I can't decide the itinerary for the trip; it has to rest with you.
我無法決定旅行的行程，這必須由你來決定。