The turning point of a story is when it goes in a different
direction, one which will resolve it. This can be different things
to different types of stories. In a tragedy, it's the point when
things start to go bad for the main characters. In a rags-to-riches
story it's the point when it seems that the hero is done for, but
then he or she gets a big break. In a sports story it's the point
when you think the Home Team is going to lose, and then they manage
to win the Big Game. In a quest story, it's the point when you
think the quest is going to fail, but then something happens which
allows it to succeed. In a detective story it is when all pertinent
fact have been established and the 'mystery' can be solved from
that point. In a love story it is when all obstacles to love have
been over-come and there remains nothing to further impede
consummation - the impediments however are the whole rasion-d'ete
(reason for being) for the story so this usually happens near the
very end.
Other words for the turning point are fulcrum, climax, epiphany
and resolve.
However, another term is "anticlimax", which means the turning
point in a story that is always a letdown. It is the point at which
you learn that the story will not turn out the way you had
expected.