Consider the value of the money involved.
Suppose we takes some cash and use it to buy stuff from Japan. What that means is we give them mere pieces of paper with writing on it and they give us in return actual goods that are useful to us. Now we have some goods, and they have some paper. What do they DO with the paper? There are two options. Either they keep it forever, or they spend it.
If they were to just keep the money (and never spend it on anything), that works out GREAT for us, because it's a lot cheaper to print extra money than to make extra stuff. If the money never came back, we could print more with impunity and never worry about inflation or ruining the exchange rate.
But in all likelihood, they'll spend that money. So again we have two options: Either they spend it on US goods and services directly or - more likely, and most relevant to your question - they spend it on goods from some other country and THAT country (or another one, after a few more hops) in turn spends it on US goods and services. The money is only valuable to the outside world because they can spend it, and when they do that it comes back to US in exchange for some good or service that we make that SOMEBODY wants.
In the case of Japan, we buy their stuff for dollars, they spend those dollars on oil from some OPEC country (they'd actually rather buy oil from Alaska - it'd be a lot cheaper to ship but we've stupidly made it ILLEGAL to sell it to them - and then the oil-producing country in turn buys stuff from us.
So when we trade, our purchasers get a good deal on the products they buy aboard and that turns into demand for other products we sell and investment in our economy at large.