Stealth Fighter missiles are equipped with bunker-penetrating capabilities. This allows them to dig into fortified structures and detonate from within, killing all occupants inside garrisoned buildings and forcing any units hiding in a Tunnel Network to evacuate.
The Bunker Busters upgrade is for the stealth fighter only. This upgrade was made available later in the conflict, following the vast deployment of GLA Tunnel Networks. Once purchased from the air field, the missiles from the Stealth Fighter will release a mid-sized blast when it hits the ground. It is made to clear out buildings that have troops inside them, and also clear out tunnel networks. It can also damage or kill infantry in the range of the blast (more damage is inflicted in the center of the blast). Also, vehicles and other known armor near the missile's hit place will fly off (e.g. Quad cannon, Technical, etc.) but doesn't receive damage when it lands, unlike the Combat Cycle.
If the general is quick reflexed, he can empty the Tunnel Network before the blast. Same thing with all civilian buildings. The blast has a 3 second delay from when the missile hit the ground to when it explodes.
Bunker Busters were originally intended for the Aurora Bomber. The voice that plays when the upgrade is finished is the Aurora's voice, and the introduction says that the Bunker Buster is an upgrade for the Aurora. It was probably moved to the Stealth Fighter because the Aurora Bomb's sheer power completely destroys most bunkers, eliminating the need to bust them, and because it fits excellently with the Stealth Fighter.