Franklin D. Roosevelt was promising that he will help lead the nation out of its current state and help America grow stronger. The other answers just don't apply to the quote.
The best answer is "that he will lead the nation out of its current state and help America grow stronger." Roosevelt gave this speech in 1932, in the darkest years of the Great Depression (but before World War II). He was promising Americans not only that he would lead them out of the Great Depression but that the suffering they'd been experiencing during those difficult years would in the long run make America a stronger nation by teaching the country certain important lessons about how to avoid the mistakes of the past.
