In financial instruments, long means trader or investor hold positive amount of security, commodity or stock with the hope that the financial instrument will rise in value. This position of holding financial instrument is also known as bullish position. It is opposite to going short, which is called bearish position.
In term of security such as bond or stock, the holder owns the security with expectation that in future it will increase in value. The bond or stock is more conventional practice of trading in going long. In term of future, going long means the holder of position buy the primary asset at contract price at expiry. The holder of position will take profit if price of an underlying asset goes up.
In forex trade market, trader usually buy or sell specific currency pairs. In Forex trading, going long means buying the base currency and selling the quote currency. For example if you go long GBP/JPY, trader is buying GBP and selling Japanese yen.