The act of greeting (or sometimes of farewell) by making a kissing gesture into the air while brushing cheeks - or in a near miss.
This gesture is usually considered insincere or childish and is a hallmark of contemporary showbiz society, especially of female American celebrities. It is often accompanied by a loud 'mwah' sound, as if to exaggerate the pretence of genuine kissing. The group that is most often associated with air kissing is that widely derided faction - the Maws (those who give their occupation as "Model/Actress/Whatever" - possibly with air quotes). The sound might well be called the 'maw mwah'.
The phenomenon has become more common around the turn of the 21st century, as has the use of actual kissing of cheeks as a greeting - something that until the late 20th century was fairly rare in America or the UK. That may be because those who use it have spent some time on their make-up and don't wish to spoil the effect. That accounts for its alternative name, the near-miss kiss.
Despite the recent popularity, the coining of the term isn't that recent. It was first cited in an article in the Chicago Tribune in 1887, which described various forms of kissing:
"Nothing is more dainty than the kiss of a wellbred chaperon, who, mindful of the time and trouble spent over the powder box, gently presses her lips on your hair just north of your ear. The minister's wife is another sweet soul, who knows where a kiss will do least harm, and her favourite method is an air kiss, with the gentle pressure of her cheek to your cheek."
The term didn't catch on at the time and didn't rise for air again until the 1970s, as here in Newsweek, March 1975:
"The uncontested Prince of American Design murmured greetings to the chic crowd, carefully air-kissing their cheeks."
See also - air quotes.