The literal sense of edacious is “relating to eating”, since it comes from the Latin verb edere, to eat. But even in Latin it had a stronger sense of voracious consumption and that was carried with it into English.
It was brought into the language — surprisingly recently — by classically educated writers at the beginning of the nineteenth century. It never really caught on and is now almost extinct, perhaps because voracious is a better established and more vigorous-sounding alternative.
The Roman writer Ovid created a maxim in his Metamorphoses: “Tempus edax rerum”, time devours everything. As a result, in its rare appearances the word is most likely to be linked with time. Thomas Carlyle used it in this way when he referred to events “swallowed in the depths of edacious time”.