The Genii A-bomb was a nuclear weapon used by the Genii.
The original shielding of the bomb was minimal. This aside, their hope was that if they could place them inside a Hive ship, an interior detonation would be capable of destroying a Wraith hive ship.
The Genii give the Atlantis expedition two of theirs bombs for in exchange received, C-4 and some of their medicines. John Sheppard was able to use at least one to destroy a Hive Ship by piloting a cloaked Jumper armed with the bomb inside (he later used a similar tactic to destroy the ZPM powered Hive Ship), surviving due to the Daedalus beaming him out. It is unknown what happened to the second bomb, but he may have simply used both.
Later Ladon Radim used one as part of his coup. He built it, planted it on an abandoned planet under a warehouse and tricked Cowen and his elite guard there. The bomb killed Cowen and his guard, allowing Ladon to overthrow the government and become the new leader of the Genii.