I'm no economist, but here is one way that war could seem to help.
In an economy, there needs to be a balance between consumption and
production. A certain level of production can support a certain standard
of living.
In practice, it seems that often these factors are slightly mismatched,
and lead to oscillations in consumption/production levels. Consumption
is a little too high (unsupportable standard of living), and then there
is a recession and consumption is a little too low (too much forced
saving). This is a vastly oversimplified picture of the traditional
business cycle.
In a war, there is more forced saving. People are called upon to
sacrifice. There may be propaganda or nationalistic sentiment which
furthers these feelings. People forego consumption which they would
normally enjoy. The excess is taxed away or donated to the war effort.
This forced saving fuels gains in production which carry on even
after the war is over. The result is rapid post-war growth.
Even though the growth is obvious, it is not necessarily worth the cost.
During the war years, people are forced to make sacrifices which they
would not have been willing to do voluntarily if there had been no war
- rationing, taxation, possibly even forced labor. Afterwards they
enjoy the benefits of the savings. But if the benefits were worth the
sacrifice, they would have saved voluntarily in order to achieve future
benefits. Since they did not do so, presumably the payoff at the end
is not worth the years of sacrifice.
Hal