You can find the answer to this question in book 2, chapter 9. Essentially, continuous war keeps the citizenry equally dependent on the government for their own rations of goods. Likewise, war means the people are united in purpose against an enemy other than the government and their is no room for large-scale revolt. A couple of further reasons that war is peace are listed below as direct quotes from the book:
War is a way of shattering to pieces... materials which might otherwise be used to make the masses too comfortable, and hence, in the long run, too intelligent.
If everyone is dumb, they will live without planned purpose to revolt. This will mean peace.
Another way that war is peace must be deduced by the reader. By reading chapter 3 of Goldstein's book, readers learn that the three superpowers go to significant lengths to put on a pretend war to keep the people believing. This great collaborated effort must take much time and tact to orchestrate. Working together so much on a common purpose quite frankly prevents the need for real war.
The war, therefore, if we judge by the standards of previous wars, is merely an imposture... though it is unreal it is not meaningless.
Goldstein admits that war is fake.
One good quote that directly states why war is peace is actually in chapter 1 of Goldstein's book:
... continuous warfare ... is also useful in keying up public morale to the necessary pitch.
This points out that the public grows in their allegiance and degree of happiness or peace as long as there is war.
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.