Foreign stock traded in the US are known as American Depository Receipts or ADR's. An ADR is a negotiable (traded) share of stock of a foreign company, where the international company has registered an ADR to trade in the united states.
Allowing an international company to have a way for it's stock to trade in america makes it easier on the issuing company. Although the American Depository Receipt must register with the SEC, the issuing foreign company does not. These can trade OTC or on an exchange. This can give a sense of stability to the stockholder. Although, as with any stock - the risk still lies with the performance of the stock and the financial well being of the company overseas.
The securities of the foreign company are deposited in a foreign branch of a US Bank. ADR holders will receive dividends in american dollars based on this banking and conversion arrangement.
Since this is still considered shares of stock in a company, the corporation will declare and pay it's cash dividend in it's natural currency, whether it is in Yen, Euro or whatever currency they use. The dividend of the ADR is then converted into american dollars and paid
out to the american shareholders.
Many securities investors own American Depository Receipt shares. It can offer you the chance to own stock in an international company, while getting the comfort of the investment being safekept in the US and traded on US stock exchanges.