The why of the title
"The Day the World Ended" is the title of a 1955 SciFi B-movie which the boy Ben had been watching at some critical time in his life. That movie had a weird looking mutant creature in it that was some kind of a model for the creature in this movie. I think the idea is Ben takes things from that movie and projects them into reality.
The title was even questionable in that 1955 movie.
http://www.imdb.com/title/tt0049128/?ref_=fn_al_tt_4
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The story is king.