Back flow preventer is one of pilot operated safety relief valve accessory which functions to eliminate the reverse flow through the main valve in case the the back pressure at pressure safety relief discharge line exceeds main valve inlet pressure.
In such condition, the back pressure would would lift the piston hence cause flow reversal from discharge to inlet line.
Back flow preventer will provide a net downward force on the diaphragm or piston to keep the main valve closed as long as the set pressure not achieved.