Amp Damage is damage that the shields add to your first shot when full
The first shot you take with a fully charge shield gets the bonus Amp Damage added to it.
When the shield recharges, it will do amp damage again, and so on, everytime time the shield has charged to a full capacity
The Amp Damage used Amp Shot Drain which is subtracted from your shield's charge.
An example shield with Amp Damage: The Bee