Computer software is broadly grouped into system software and application software. System software is the layer that manages the computer's own hardware resources, such as the processor, memory, storage devices, and input/output ports, and it provides a controlled environment on which other programs can run. The operating system is the main example of system software.
Application software, by contrast, is written to perform tasks for the end user, such as word processing or accounting, and it relies on system software to communicate with the hardware; it does not manage the hardware directly. Because system software sits between the physical hardware and the applications that request services from it, translating high-level requests from applications into instructions the hardware can execute, it is the software that acts as the intermediary between hardware and applications.
Firmware is a form of system software permanently stored on a hardware device to control that specific device, and it does not manage the general relationship between all applications and all hardware the way an operating system does, so it is a narrower and less complete answer here.
Examination reminder: whenever a question describes software that "manages," "controls," or "coordinates" hardware for other programs, the expected answer is system software, with the operating system as its central example.