The motif of the clock stopped at 8:15, the indelible kiss (of the heat flash from the bomb blast), and the call of 'conditions normal,' all reference that sense of history frozen on the precipice of armageddon. The song looks back almost wistfully to the point in history when that state of existence was brought into being. The song is even more specific - it is about living in the 1980s under the shadow of Cold War fears of atomic war and nuclear annihilation, which many people at the time viewed as inevitable given the way world events seemed to be going.
The other posters who point out the obvious reference to the atomic bomb dropped on Hiroshima ('Little Boy'), and the evocation of the imagery of a mother and her child as an ironic metaphor for the relationship between the bomber and the bomb, are all correct. General CommentThe Cold War was the subject of many 80s synthpop songs, among which 'Enola Gay' is one of the best known.