This issue has come up about 1,200 times in the last five years for me, so I suppose it warrants at a minimum a brief discussion. Ideally, I should like to give it a little more justice than this, but once you go down this road, it can be endless unless you cut it off at a certain point.
Without discussing the finer points of how changes in foreign exchange rates impact your investments, let's use a simple example. In this fictional example, you buy 100 shares of Petrobras (PBR) in Brazil at $35 a share. The Brazilian currency, the real, is trading at 2.00 to the dollar. Whether you bought it on the Sao Paulo exchange or as a New York listed ADR (American Depository Receipt), it is still effectively denominated in the real. So long as the real remains at 2.00 to the dollar, changes in the underlying price of Petrobras should still have a 1-1 translation in dollar terms. In other words, if Petrobras rises by $1 in Sao Paulo, you shares, either there or here, should rise by that same $1 (or 2 reals). There is some break in the link with ADRs from time to time, but over the long run they correlate pretty well. ADRs are supposed to incorporate changes in foreign exchange rates in their valuations, but some times things go slightly awry.
However, what happens if the Brazilian central bank cuts interest rates, making in the interest rate differential between the U.S. and Brazil look less attractive so investors start selling real denominated assets? Well, here you can get a double whammy. Because there is a general flight from Brazilian assets, Petrobras may decline from $35 to $30. In other words, your asset fell from $3,500 to $3,000 or from 7,000 to 6,000 in real terms. However, the liquidation of Brazilian assets put pressure on the real too. Let's say the real weakens from 2.00 to 2.25 to the dollar.What does this do to your assets now? Well, they're still worth the 6,000 in real terms, but in dollar terms they are worth 6,000/2.25 or $2,667 (rounded). You lost $500 on the actual decline and $333 on the decline in the currency.
While this seems like a stylized example, it really actually isn't. Moves of greater magnitudes than this happened in Brazilian assets for much the same reason in mid-2006 because of nearly the same cause(the Fed was raising rates while Brazil was cutting and the real routed for a brief period as a result). Currencies move for a variety of reasons, but interest rate differentials, or rather the prospect for changes in differentials, are one of the major short term reasons. Of course, in the long run, current account deficits, the relative attractiveness of all forms of investment, political stability, and so on are major contributors. Economists have their own views on the subject as well relating to interest rate parity, which actually has the opposite conclusions of what we often observe over the short term in the markets.
Whatever the possible causes, which we can all discuss later, these are the effects and they bear watching. If an investor is blind to moves in the foreign exchange markets while investing in foreign denominated assets, they can get burned. Of course, if you are a U.S. investor and the dollar seems set to weaken for years to come, overseas investments are more attractive that ever. You get the superior profit growth of emerging markets plus the weakening of the dollar which automatically raises the value of your foreign investments. Of course, if you bet wrong, then your returns get clipped.