e.g. Indian rupee kept in a Malaysian bank is an example of eurocurrency deposit.
Eurocurrency market is mainly used by companies and people who wants to bypass certain regulations.
It is a well understood phenomenon that a riskier investment demands a higher return for it to be attractive to investors (assuming the investors are completely rational in their decision making). Therefore, given that the Eurocurrency depositor is not protected by domestic banking laws, it is a riskier investment and warrants a higher return and therefore the rates on deposits are higher than in the domestic market. These are not protected by domestic banking laws and do not have a governmental deposit insurance.