Thayer's Greek Lexicon

 1. investigation, inspection, visitation
  1) that act by which God looks into and searches out the
ways, deeds character, of men, in order to adjudge them
their lot accordingly, whether joyous or sad
  2) oversight
1b1. overseership, office, charge, the office of an elder
1b2. the overseer or presiding officers of a Christian church