The term "wartime state" refers to the changes that were made by the government to mobilize both popular opinion and economic activity to aid in the war effort.
In the United States in WWI, the government felt that it was important to have the public be solidly behind the war. This led to efforts to shape public opinion through propaganda that was created by the Committee on Public Information. Efforts were also made to control dissent through such things as the Sedition Act.
The US also felt that it was important to get industry to produce the things that the armed forces needed. In order to do this, the government entered into a close relationship with industry in a way that it had never done before. The two coordinated closely to ensure that necessary war materials be produced.
This was the wartime state. It was a system in which the government took on new powers and entered new relationships, all in an effort to make the war effort run more smoothly.