Definition of the term "air
When a player has the best possible hand, he is said to have the "nuts". Having "air" is exactly the opposite. When you have air, you do not even have a pair. When a player has air, he can play conservatively and fold or go all in (bluff with air).
Example of a situation where a player has "air
Sometimes a player is left with air, but had incredible potential with his hand. Let's say you have a nine and a ten in hearts preflop. The flop is 7 of hearts, 8 of hearts and 2 of spades. Here you have a monster draw. All 6s or jacks will give you a straight, all hearts will give you a flush, all nines and tens will give you a pair. In this situation, if you are in position on the flop and have the lead (you are the preflop raiser), you will want to bet. Let's say you bet on the flop and your opponent calls the bet. If the turn is still a brick (a card that is not significant to you), you will probably bet again. And if the river is a brick again, you might have the reflex to bet big on your "air" in hopes of getting your opponent to fold.