What do(es) the quote(s) "War is peace, freedom is slavery, and ignorance is strength" mean?
The answer rests with the paradoxical nature of the Party itself. How it rules is the exact opposite of how its propaganda says it controls.It goes directly into the concept of doublethink, which Emmanuel Goldstein explains through the word "blackwhite":
But it means also the ability to believe that black is white, and more, to know that black is white, and to forget that one has ever believed the contrary. This demands a continuous alteration of the past, made possible by the system of thought which really embraces all the rest, and which is known in Newspeak as doublethink. Doublethink is basically the power of holding two contradictory beliefs in one's mind simultaneously, and accepting both of them.
Thus, according to the Party, "war is peace" means that they continually "fight" wars in order to keep peace at home. During times of war, nations generally unite. Of course, if the people are focused on a common enemy, they are much less inclined to notice how unhappy they are in their own lives. So they make less trouble for their government. "Freedom is slavery" can be thought of in the same way. the slavery of Party members equals freedom for Party leaders. Finally, "Ignorance is strength" can be read "Your ignorance is our strength", again meaning that the ignorance of the people translates into the strength of the government.
This quote is also the reader’s first encounter with the idea of double think, the party process of weakening an individual mind’s strength and independence and forcing them to live in a constant state of propaganda induced fear. Through double think, the government is able to force its people to willingly accept basically anything they say, even if it makes no sense whatsoever. For instance, the Ministry of Peace is in charge of waging war, the Ministry of Love is in charge of political torture, and the Ministry of Truth is in charge of doctoring history books to reflect the Party’s ideology. This slogan is an important symbol which shows the hidden power of the government over its people by saying that even though the slogan is completely illogical, the people are psychologically so influenced by the government that they turn a blind eye toward anything else. In other words, the government is able to convince people that “war is peace” by telling the people that having a common enemy helps keep the country together in many ways, but it was mostly because of the fact that since there is war, everyone will be afraid which will allow the government to control them easier resulting in peace. With “freedom is slavery” they explain that they will succeed only if they are united, if they try to go off on their own, then they will fail. By the same token, “Slavery Is Freedom,” because the man subjected to the collective will is free from danger and want. And “ignorance is strength” because the more people ignore the contradictions of their slogan, the more powerful the governments power gets over its people.