Refers to public masturbation.
Can also be used to refer to any scandalous, embarrassing, or humiliating act performed in public, which act is followed by media attention and public scorn.
This phrase gained popularity following the infamous incident on United Flight 340 to Denver in mid-May, 2011, where an individual reportedly masturbated "to the point of ejaculation" while sitting in row eighteen. He was subsequently arrested and faces criminal misdemeanor charges.
That dude Row Eighteened it at work! I hear the receptionist is going to need therapy.
I'm going to drink some Four Loko and start Row Eighteenin' it at the club tonight.
I can't believe that guy just streaked through Wrigley Field and urinated on second base. He must have been sitting in Row Eighteen.