SPD005G is a bridge gauge type pressure sensor which measures pressure with respect to atmospheric pressure. Its measuring limits are from 0 to 14.5psi. Interfacing such sensor require some conditioning circuit that is build out of three operational amplifiers.
Differential signal from sensor enters two amplifiers that are used as buffers for next standing differential amplifier. Differential amplifier simply gains differential voltage which then enters to Arduino A0 input. Arduino converts input voltage in to mV that is displayed on LCD. If you need to display value in Pa or psi, then you probably need to do calibration with known reference.