Sator-rotas: understanding an ancient viral meme

This year’s Hallowe’en posting proposes an original plausible interpretation for a famous but superficially nonsensical Latin phrase. The oldest extant examples of the text are about 2000 years old, graffiti from Pompeii, five words of five letters apiece, four of them ordinary Latin words, arranged in a word square:

R O T A S
O P E R A
T E N E T
A R E P O
S A T O R

Sometimes the square is found written in the reverse order (or if you prefer, rotated ninety degrees either left or right – the result is the same regardless):

S A T O R
A R E P O
T E N E T
O P E R A
R O T A S

Through the centuries since Pompeii, versions of the square have been placed in a variety of settings, from chambers hidden within Christian churches, in aged books of magic spells, and as a spirit medium’s chant in Tales from the Crypt on television.

Now, what could something like that mean?