Thayer's Greek Lexicon

 1. an overseer, inspector
2. spectator, eye witness of anything

This was the name given to those who had attained to the third, i.e
the highest grade of the Eleusinian mysteries; these were celebrated
annually at Eleusis and Athens in ancient times, in memory of the
abduction and return of Persephone and in honour of Demeter and
Bacchus.