Overflow pipes are simply pipes that will drain the grow beds before they overflow onto the ground. The pipes are set slightly above where the siphon would normally trigger and run through the side of the grow bed and back to the sump. If for some reason either of the siphons should fail, the water will run back into the sump and keep the system running. It wont be ideal but the fish will be happy and the pump will be happy. The plants should be fine as long as the beds don't stay flooded for too long.
They should never be needed but for the sake of $5 worth of fittings its worth adding them.
For an additional few cents a very small hose can be connected from a hole in the bottom of each grow bed to the overflow pipes so that there is always a small constant stream of water draining from the grow beds to the sump. This is done in case the main pump fails. In the event of the main pump failing, the garden beds could be half full of water and the plants can suffer as a result. The slight leak allows the beds to drain albeit over a few hours.
Main pump fails -
grow beds slowly drain and will be fine for up to 3 days (plants and bacteria) depending on weather.
fish are fine because the powerhead keeps the oxygen levels up.
Power head fails -
doesn't bother the fish as the main pump is still doing it's thing.
doesn't bother the grow beds as they don't get any water from the power head.
Siphon fails -
water overflows through the overflow pipes back into the sump so sump pump is fine.
gardens are flooded but they can take that for a while depending on the plants (eg. lettuce can grow in permanently flooded beds)
Within an aquaponics system its always good to have backups for whatever critical systems you have, especially when they can be done for a relatively small cost.