The fuel pump relays job is to act as a switch to turn on and turn off the fuel pump when needed.
When you turn the key on the fuel pump should come on for a minute to allow fuel to get to the fuel injectors and then it should turn back off until you turn the key to the start position.
When you turn the key to the start position another part of the fuel pump relay should switch the fuel pump back on to provide fuel pressure to start the car.
After it's running the relay should keep the fuel pump running so the engine gets enough fuel to stay running.
When the fuel pump relay goes bad it may cause the car to not start at all because it's not turning on the fuel pump.
Your engine could also stall out due to the fuel pump relay going bad suddenly and then the engine may fail to start again.
The most common symptoms of a bad fuel pump relay is a no engine start or engine stalling or you hear no noise coming from the fuel pump.