"Is he a priest?" implies a certain familiarity with the subject. You know who you are talking about, you have an interest in him, you think he might be a priest but you don't know for sure, so you ask: "Είναι παπάς;" Now, picture a beautiful Sunday afternoon. You take a walk in a busy square in the centre of Athens with a friend, when you suddenly notice this guy in the crowd who seems to be dressed like a Greek Orthodox priest. You point at him and ask your friend: "Is that a priest?" or, if your friend speaks Greek "Είναι εκείνος ένας παπάς;"
@jaye16: The relationship between "αυτός,-ή,-ό/εκείνος,-η,-ο" and "he/she/it/this/that" can be confusing to many people. Thank you for your contribution to a great Hellenic learning tool!