In Chapter One of 1984, what do the three slogans of the Party mean?
The reader is introduced to these seemingly nonsensical party slogans as Winston reads them on the Ministry of Truth building. There is some obvious great irony that a ministry that proclaims itself as the purveyor of truth should produce such slogans as, "War is Peace, Freedom is Slavery, Ignorance is Strength" (p.6). It surely makes a mockery of what any reasonable minded citizen would understand as logical thought, but therein we gain some understanding of the totality of control that the government of Oceania exercises.
Just as Newspeak seeks to mould the very language of citizens to produce the government's desired outcomes, the meaning, the production of the three slogans is designed to twist the citizen's logic into accepting previously thought of undesirable aspects of humanity (war, slavery, ignorance) as normal or even as a virtue. In order to reinforce the citizenry's acceptance of the new logic (and override the natural human desire to question the logic of the slogans) the state employs such apparatus as saturation propaganda, police terror and torture, and public events like Hate Week.
The party slogans foreshadow what is to come. O'Brien's torture of Winston involves curing Winston of his supposed insanity of not accepting party logic. We learn during Winston's torture that the Party can successfully change 'truth' to whatever purpose it wishes - a truly chilling exercise of power.