You can certainly explain even something as sophisticated as quantum field theory to laymen if you take the right approach. Feynman did just this in his lecture

You can certainly explain even something as sophisticated as quantum field theory to laymen if you take the right approach. Feynman did just this in his lectures on QED, now available in book form. He didn't use any math, even though he talked about his own solution to the entirely mathematical problem of renormalization in QED.