Theater and acting represent ideas of deceit, lies, illusion, and fantasy here. Art really imitates life as all the characters who act in the play at Mansfield are either great actors in real life, are being deceived by those around them, or are deluding themselves. Characters like Henry are often described as great actors. This has important double meaning for Henry. He's good at acting in the theater, but he's also dangerously good at fooling people in real life and manipulating them. His real-life acting ability made both of the Bertram sisters fall in love with him, for example.
Acting and the theater are also tied to themes of fantasy and deception. During the play, a lot of characters are fooled by those around them. Maria thinks that Henry was serious about her during this time, for instance. But the theater also helps to reveal some painful truths to people. Julia discovers the truth about Henry while Mr. Rushworth begins to suspect that Maria doesn't love him, though this suspicion didn't help him out in the long-run.
And the characters who act in the play lie to themselves as well. Fanny, the only one not acting, observes everyone else and is upset to see that Edmund is joining in:
Could it be possible? Edmund so inconsistent. Was he not deceiving himself? Was he not wrong? Alas! it was all Miss Crawford's doing. She had seen her influence in every speech, and was miserable. (16.28)
As the only character not acting, Fanny can serve as a key observer of such things. But Fanny's repeated insistence that she cannot and will not act offers other important meaning. By saying she cannot act, Fanny makes her refusal sound like it isn't a choice. Fanny is literally incapable of acting, and not only in the play. Acting here also refers to action, movement, and non-passive behavior. As we know, Fanny is typically extremely passive, and she basically announces that she cannot take action during the theater chapters.