This interpretation of
quantum mechanics is named after the city where its creator
Niels Bohr worked and lived. It is the
principle of
complementarity taken a step further.
Trying to explain the results from the
double-slit experiment/
wave/particle duality are hard in our thought world. The view of Bohr was that theories should be strictly based on
experimental observations, and not inhibited by limitations in our philosophical system and imagination. The indeterminacy of said experiments and
Heisenberg's uncertainty principle for instance should be seen as real and physical, and not the effect of imperfections of the theories.
This interpretation is what had Albert Einstein say
God doesn't play dice
but dear old Einsten was in fact proven wrong. God does indeed play dice. See Einstein-Podolsky-Rosen paradox for more on that.
One famous theory that follows the Copenhagen interepretation is the one that there are many universes. It was introduced by John Archibald Wheeler in 1957. His idea was that everytime a choice is made on the microscopical level, the universe is split up so that every possible occurence actually happen in one universe. Or to put it in the Schrödinger's Cat scenario: In one universe that cat is alive, in one it is dead.