Lately, I find myself telling my students: "assume your audience doesn't know anything" (this is an improvement on the original: "assume your audience is stupid").
Now I don't mean that you as a performer ought to look down upon your audience. Nothing high-brow or elitist helps anyone who's supposed to be an ambassador for their art of their ideas.
What I do mean is that you want to be absolutely clear to your audience what your musical ideas are. Something I've learned over and over again is that my musical ideas might seem clear to me, and I might think that I'm expressing them clearly. But usually those ideas have to be exaggerated for my audience to understand them.
Assume your audience knows nothing about classical music. Express your ideas in as big a way as necessary to make it abundantly clear to them what your musical intentions are, what story you're trying to tell.
This is how we get an intentional pianist, someone who's artistry is communicative and engaging.
"Modern performers seem to regard their performances as texts rather than acts, and to prepare for them with the same goal as present-day textual editors: to clear away accretions. Not that this is not a laudable and necessary step; but what is an ultimate step for an editor should be only a first step for a performer, as the very temporal relationship between the functions of editing and performing already suggests." -Richard Taruskin, Text and Act