To have airs is to be condescending or arrogant — in other words, to act like you think you're better than other people. If you put on airs, you'll find it hard to make friends.
It's most common to find the word airs in the phrase "to put on airs." This basically means to act snobbish or stuck up. Someone who puts on airs is extremely annoying to everyone around him, clearly pretentious and mannered in his attitude. The phrase has been around since the 1780s, and it comes from the French air, "look, appearance, bearing, or tone."