A trader is in a LONG POSITION when she buys a currency pair. Shorting is the opposite of going long. The trader is in a SHORT POSITION when she sells a currency pair.

For example, when a trader buys EUR/USD, she is "longing" the Euro while at the same time "shorting the US dollar. If she were to decide to sell EUR/USD, she is "shorting" Euros and "Longing" the US dollar.

These colloquialisms are popular among traders in the Forex Market in leiu of the terms 'buying' or 'selling.'