Doublethink (or ”Reality control” in Oldspeak) is to hold two contradicting thoughts in your mind which both are true.
”To know and not to know, to be conscious of complete truthfulness while telling carefully constructed lies, to hold simultaneously two opinions which canceled out, […] to believe that democracy was impossible and that the Party was the guardian of democracy. […] Even to understand the word ‘doublethink’ involved the use of doublethink.” (p. 34, ll. 17-30)
”And if all others accepted the lie which the Party imposed—if all records told the same tale—then the lie passed into history and became truth. ‘Who controls the past,’ ran the Party slogan, ‘controls the future: who controls the present controls the past.’ And yet the past, though of its nature alterable, never had been altered. Whatever was true now was true from everlasting to everlasting.” (p. 34, ll. 5-11)