Spiritual Meaning:
A bomb exploding in dreams often forecasts an unexpected event.  Dreaming of a bomb would appear to suggest a fear of sudden death or a cataclysmic event.

Psychological / Emotional Perspective:
Psychologically, we need to be aware that our own emotions are  likely to get the better of us. Anger, for instance, can be a particularly destructive force.
Everyday Material Aspects:
Bombs appearing in a dream usually indicate some form of explosive situation with which we need to deal. Exploding a bomb indicates the need for positive action, while defusing a bomb suggests taking care not to make a situation worse.

Also consult the entry for Atom Bomb, Explode / Explosion, Nuclear Explosion and War.