It happens before. So, at the moment you encounter the weapon, spell, or item, you play Fiery Glare, banish the encountered card, then (if you want) explore again.
Except that the recovery pile wouldn't be used for the encountered weapon, spell, or item. The recovery pile is only used for cards that you play (if they have a during recovery power). Since the encountered card is banished as a result of another power (Fiery Glare), they don't go into the recovery pile. Fiery Glare would go into the recovery pile after it is played, but the encountered weapon, spell, or item is returned to the vault as a result of playing Fiery Glare.
At least, that's how I read it based on the posts above, the Core Set Rulebook, and the Core Set Conversion Guide. Perhaps I'm misinterpreting or there's some other guidance that I've missed ... ?
+1 to all responders here.
Just to clarify: Hang Zhu, I wonder if you are confused about what "it" refers to in your quoted card text:
When you encounter a weapon, a spell, or an item during your exploration, discard this card to banish it; you may explore again.
"It" is the weapon, spell or item you encountered. If you play Fiery Glare when you encounter the weapon, spell, or item, you banish the card you encountered immediately (as Brother Tyler says). What happens to Fiery Glare is a different question (which Jenceslav accurately explains). Finally, as Hawkmoon says, after the encounter you may explore again, but you have to do so immediately or else you lose the opportunity granted by Fiery Glare.