The currency carry trade is created by simply borrowing funds at a low rate and investing these funds into higher yielding assets. A very relevant example can be seen in the famous "yen carry" trade in which Japanese Yen are borrowed at an interest rate which is next to nothing and invested into higher yielding US treasury bonds. The interest rate differential between the two is a bit over 300 basis points. As you can see, investors using leverage stand to make quite a bit of money.
There is a catch, however, there are no free lunches. The currency carry trade has the risk of currency exchange rate uncertainty. If the dollar were to drop dramatically against the Japanese Yen, you can see how a heavily leveraged position in US dollar denominated securities would pose a problem to the security holder when the bond matures and it is time to pay back the loan in Japanese Yen.