Overnight interest is only applicable to margin trading. Trading on margin means that a trader borrows money to buy or sell a market instrument using actual account value as collateral. Traders generally use margin to increase their purchasing power so that they can own more market instruments without fully paying for it.
Considering that trading on margin involves borrowing money, trader has to pay interest on the loan. That interest is referred to as Overnight Interest and is generally charged based on number of days a position on margin was held. Most trading systems will charge daily interest portion at the end of each trading session and charge three times more on Monday or on other preset weekday (if market is closed on weekends).
In case of currency trading, Overnight Interest is calculated as interest rate differential between interest rates for particular currencies that make the currency pair that is being traded. For example, if a trader wants to sell USD/JPY on margin, he or she will have to pay 4.0% (e.g. U.S. interest rate at 5.0% subtracted by Japanese interest rate at 1.0% makes the interest rate differential) of the amount borrowed per year to hold the position.
Before trading on margin it is highly recommended to get information on exact interest rates charged for borrowing money and how that will affect the total return on investments.