Exchange-rate risk is the risk of receiving less in domestic currency when investing in a bond that is in a different currency denomination than in the investor's home country.
When investors purchase a bond that is designated in another currency other than their home countries, investors are opened up to exchange risk. This is because the payment of interest and principal will be in a foreign currency. When investors receive that currency, they have to go into the foreign currency markets and sell it to purchase their home currency. The risk is that their foreign currency will be devalued compared to the currency of their home countries and that they will receive less money than they expected to receive.
As an example, suppose that a U.S. investor purchases a Euro denominated bond. When the interest payment comes due and if the Euro has declined in value compared to USD, the investor will receive less in USD than expected when he or she transacts in the foreign currency markets. In short, the investor will receive fewer Euros to purchase USD.