As the actors are acting out the play, Claudius asks Hamlet what the play is about. In lines 265-267 Hamlet says, "Your majesty and we that have free / souls, it touches us not. Let the galled jade wince; / our withers are unwrung."

What does Hamlet mean by this?

Hamlet means that whoever is guilty of the crime committed in the play will wince.

Explanation:

Hamlet here is testing his uncle Claudius for the possibility that he may have killed his father which he already did suspect him for.

He is only able to confirm his concerns when it so happens that Claudius winces when he sees in the play the reenactment of how he got his brother killed.

This happens after hamlet warns him so so the men both understand that this is going to be the situation now. Hamlet's worries are confirmed and now he knows for sure who killed his father.