What does it mean when you trade a “long” position? What does it mean when you trade a “short” position?

When you buy an asset, you are going “long”. When you sell, you are going “short”.

Example: Sam buys stock, so he has opened a long position.

When you trade currencies, you buy one currency and simultaneously sell another currency. So you are going long for one currency and simultaneously opening a short position for another currency.

Example: When Sam buys EURUSD, Sam is going long for EUR and going short for USD.