A long position means a trader has bought a currency expecting its value to rise. Once the trader sells that currency back to the market (ideally for a higher price than he or she paid for it), their long position is said to be ‘closed’ and the trade is complete.
If you wanted to open a long position on the Euro, you would purchase 1 Euro for USD 1.1918. You will then hold your position in the hope that it will appreciate, selling it back to the market at a profit once the price has increased.
A short position refers to a trader who sells a currency expecting its value to fall and plans to buy it back at a lower price. A short position is ‘closed’ once the trader buys back the asset (ideally for less than he or she sold it for).
In this case, if you think the Euro will weaken against the Dollar, you will sell 1 Euro for USD 1.1916 and hold a short position. You expect the Euro to depreciate and plan to buy it back at a lower rate.