The nukes are two(Alpha & Beta) nuclear-armed explosive devices used to alter the course of Attilla, in order to prevent it from hitting the Earth.
The very first puzzle in the game consists of removing the nukes from the Pig, finding appropriate quadrants on the asteroid's surface to plant them on, arming them, and setting them off. The explosion opens a huge fissure in Attilla's surface which Boston Low, Maggie Robbins & Ludger Brink will then enter.