Wikipedia
Eurocurrency
Eurocurrency is deposits in banks that are located outside the borders of the country that issue the currency the deposit is denominated in. For example, a deposit denominated in Japanese Yen held in a Brazilian bank is a Eurocurrency deposit. Likewise a deposit denominated in US dollars held in a Singapore bank is a Eurocurrency deposit, or more specifically or more clearly a Eurodollar deposit.
Eurocurrency does not have to involve either the euro currency or the eurozone.
Today the Eurocurrency and Eurobond markets are active because they avoid domestic interest rate regulations, reserve requirements and other barriers to the free flow of capital.