Meaning to stray from the accepted norm, or to do something contrary to established patterns of behaviour.
Strangely enough, although most people who have heard this phrase have assumed that it means to stray from the beaten path (as in the path that has been beaten clear by the volume of people following it). However, its etymology, is even more obscure than that as it in fact refers to Mrs. Beaton's "Book of Household Management", that was first published in 1859.
Whilst purporting to be about household management, most people would recognise it as what we now call a cookbook. The book rose so quickly to acclaim in British households that it became the mainstay of British cookery for over 75 years (even as a Brit, I have to wonder what the hell was in it to make Old British food so bad for so long).
To go off the Beaton Path originally meant to create a dish that was not contained within Mrs Beaton's book.