The ignition amplifier takes a small low current input signal and switches a high current signal on the output to ground (hence amplifier).

Here it 'charges' the ignition coil primary by pulling it to ground, this typically lasts 2-6ms, the ignition amp then releases the now saturated primary. Now you see a large flyback voltage which is clamped by the ignition amplifier to 350-400v. This high voltage flyback voltage is stepped up by the ignition coil/transformer to several thousand volts on the output of the secondary.... where you get spark.

The ignition amp replaces the points and condenser in an old school distributor setup and is still used in modern cars either inside the ecu, as an ignition amplifier or right on the coil its self for coil on plug setups.

It does not do anything to do with the fuel pump of fuel system.