Quinine works against Plasmodia falciparum (and I suppose other Plasmodia) by preventing the Plasmodia from protecting itself against haem. Haem, which is a byproduct of the breakdown of haemoglobin, which Plasmodia consume, is poisonous and so Plasmodia store this in a vacuole, so they can transform it into harmless haemazoin. Quinine however, interferes with the storage of haem (but I couldn't find exactly how it does that) so that it remains in the cell, poisoning, and, eventually, killing it.
Hope that helped.