What is the importance of doublethink to the Party's control of the citizens of Oceania?
Doublethink is a form of "reality control" in which people accept two ideas, even when these ideas are contradictory. For the majority of the novel, for instance, Oceania is at war with Eurasia but, suddenly, during Hate Week, the Party declares that it is fighting against Eastasia and always has been.
You will notice from the text that nobody questions this sudden change, even though they can remember the war against Eurasia. This is why the Party is so successful in maintaining control: it manipulates the popular understanding and perception of the past and the people of Oceania willingly accept it because they have been brainwashed to do so. On a practical level, this means that the Party can do as it pleases, safe in the knowledge that nobody will ever question its actions.
This is, perhaps, best summed up in the following quote from Emmanuel Goldstein from Part Two, Chapter Nine:
"For the secret of rulership is to combine a belief in one’s own infallibility with the power to learn from past mistakes."