When the pop bumper driver board is in the machine and you're not sure the board is getting power, it's a real pain to stick your meter leads into the connector to measure if there's 5 volts on the board while trying to hold/balance/prop the playfield. Having the green LED on the board lit up will instantly tell you at a glance the board is getting power. The LED's are great for "in-machine" testing.
Say you're troubleshooting a non-functioning pop bumper that appears to be "dead" when you close the spoon switch. The yellow LED on the board will flash once each time you close the spoon switch. This indicates three things have occurred:
1. The board has received a valid switch closure signal from the pop bumper's spoon switch.
2. The board has turned on the pop bumper driver transistor.
3. The coil operating voltage (pulse) has been sent to the coil and the coil should move.
So if the yellow LED flashes and the coil does not move, then you have either a bad coil (open circuit) or the wiring between the pop bumper driver board and the coil is bad (open wire).