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It's hard to think about a how an explosion has momentum conserved because an explosions blows up everything in little pieces.  However, those infinite amount of pieces all contribute to conserve the momentum of the explosion before it exploded.  The law of conservation has a simple equation of mass times velocity initially equals the mass times velocity final.  An explosion before it happens is equal to zero because it has no velocity at all.  After the explosions, the pieces broken off in the explosion will go everywhere.  The direction of the pieces matter because after the explosions, the direction of the pieces will have equal magnitude but just in the opposite direction.  So when you had up all of the individual pieces of its direction, mass and velocity, the pieces will even each other out.  Therefore the sum of all of the infinite pieces after the explosion will have a momentum equaling zero.  Therefore the momentum of the explosions is conserved.  It's crazy to think that the aftermath of an explosion has zero momentum.

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