There are at least two possible reasons for this.
In 1916, when Wilson was running for reelection, he had a campaign button that called him the "man of the hour." This was before US participation in WWI, of course. In that case, he was referred to in that way because of his work in helping American workers get shorter hours and better conditions.
Later, he could have been called the man of the hour because of his attempts to make the Paris Peace Conference into a force for reforming the world. He was trying to get his 14 Points implemented. He did so in an attempt to create an ideal world where war would be less likely to happen.