The continuity equation expresses the conservation of mass, so the total amount of m. entering must be equal to the total amount leaving. For a single flow device the mass flow rate is constant through it, so you have the same mass flow rate across any total cross-section of the device from the inlet to the exit.
The volume flow rate is related to the mass flow rate as
so it can vary if the state changes (then v changes) for a constant mass flow rate.
This also means that the velocity can change (influenced by the area as V = VA) and the flow can experience an acceleration (like in a nozzle) or a deceleration (as in a diffuser).
