I think that the easiest way to explain it, to someone with NO formal musical background is in the overall feel. Tell them that Romantic music sounds somewhat like a film soundtrack (sort of), and that Baroque sounds more like a dance in a medieval castle, (not really, but...)
It's the vibe, that the average person who isn't familiar with theory or classical musics is going to respond to. Tell them that Romantic music is flowy and dramatic, Baroque music is rhythmic and hypnotic. Tell them that Romantic music is the Nutcracker, and Baroque music is what Tenacious D starts out with, singing about Bach and Rock.
Of course, the easiest way would be to just play them some music from the corresponding periods...
-Zack
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