The Annihilation Barge is essentially a massive gun mounted on a hover platform that performs as a tarpit killer. Usually found in the lower levels of a Tomb World, anyone who SOMEHOW manages to avoid hungry, hungry Scarabs, massive Spyders, ghastly Wraiths or even the Necrons themselves will more than likely be facing the receiving end of the Tesla Destructors; one eldritch discharge of green lightning later and you'd be turned to dust...
According to the fluff, they were most often fielded by the Akannazad Dynasty Tomb World against the Orks of Charadon, tearing the armour from the Trukks and the Looted Wagons and incinerating their Boyz. They were also used in the Orphean War by the Maynarkh Dynasty against the Imperium of Man.
Using the same Quantum Shielding panels and skimmer technology as other Necron vehicles such as Doomsday Arks and Ghost Arks, Annihilation Barges are extremely durable but due to their low speed they are used defensively. The vehicle's primary weapon is a twin Tesla Destructor, which utilizes the same 'Tesla' lightning as the Tesla Carbines and Cannons. This weapon can wreak havoc amongst infantry as their flesh is roasted and their blood boils (in-game, every roll To Hit of a 6 adds two additional hits). For secondary weaponry the vehicle can mount either a Tesla Cannon or a Gauss Cannon.
Unfortunately, while the Tesla Destructor is terrifyingly effective against non-power-armor armies like Orks and Guard, it struggles against units with high armor saves. In 8th Edition, it is arguably a poor choice over Necron Immortals who could bring tesla to the field cheaper and in greater numbers. In 9th, it continues to suffer from not having enough punch to be really competitive in a power-armor-heavy meta. For only 20pts more per model, you could get a really strong Canoptek Doomstalker with devastating anti-tank fire and very strong rules and synergies.