They rely on exports.
So they would want a weak currency at home vs. the world where their products are sold. So if they can make a product for 10 yen and sell it in the US for 10 dollars, bringing home those 10 dollars at 1:1 would yield 10 yen and no profit, but at 5:1 exchange rate they can bring home 50 yen and a near 400% profit. The weaker the yen (vs the target currency) the better.
The reverse works for a country relying on imports. And of course it all varies on internal cost of living and salaries and so forth. Ideally you have an economy that exports high end goods (cars, computers) but does not import basics (food/fuel). Thus you get home grown "cheap" necessities for the population, and have high quality education, jobs and make high quality export products.