What does ‘Gag’ mean?

There are two ways to use this. First, as a synonym for a punchline or joke. For instance, “La La Land was announced as the winner of the 2017 Oscar for Best Picture, but the gag is that Moonlight actually won.” The other way is based on its traditional definitions, one of which is to choke. If someone is so good, or so shocking, you’ll gag over it: “Look at Meghan Markle in that tuxedo jacket. I’m gagging!”