When the bomb goes off, the air immediately around the blast becomes superheated and rises rapidly (as all hot gases do). Normally, the fireball would be spherical, but that fast-moving upward air causes a vacuum underneath, which causes cooler air on the ground to rush inward to fill the void. The result is that the fireball at the base is being blown inwards while the fireball at the top is still rising outward. Hence the mushroom shape.
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