What do we mean when we say it today?
The average Joe Schmo wouldn't go around saying he'll put on an "antic disposition" today without knowing it was Big Willy he was quoting. Most of us automatically think Hamlet as soon as we hear this quote. It's just become that iconic. The quote has outlived the scene in a lot of ways, just like the performance Hamlet is referencing.
So Hamlet decides to act like a different guy whose totally lost it so he can learn the truth about his uncle murdering his dad. Cool. But his little phrase "antic disposition" has taken on a life of its own. It's not about madness or duping his uncle into believing him anymore. Nowadays, it's about the performance of madness. Or, to put it another way, this one is about how we can really pretend to be something we're not. It's a part of the stage, and a part of everyday life.