A back pressure valve is a control valve that is designed to hold back pressure on a process. This would be desirable to hold a certain level in a vessel or hold a gas pad above a tank.
Another function of a back pressure control valve would be to hold a centrifugal pump on its curve. A centrifugal pump will only provide a flow rate based on downstream pressure, In order to lower the flow rate of the pump, an artificial pressure drop is introduced with a back pressure control valve. This pressure drop will cause the operating point of the valve to move. When the valve is used for controlling flow on a pump, it is called a "Flow Control Valve" or FCV on the P&IDs. It should also be noted that the same functionality can be achieved by using an Adjustable Frequency Drive (or Variable Frequency Drive) which speeds up or slows down the motor based on flow rate. Using an AFD will have lower operating costs than a pump with a control valve.