What does it mean to be long or short?

No, it's got nothing to do with what you're thinking ;-) If your analysis shows that the base currency will rise, then you buy. This open trade is called a long position. Why long? Because it can go up endlessly (at least theoretically).

Conversely, if you think the base currency of a certain currency pair is going to get weaker, then you sell and you've got a short position on your hands. It's called short, because the value of a currency cannot go below 0 into infinity. The road downwards is finite. Finite is always shorter than infinite.

Long and Short Forex Positions