This is a topical word: the cardinal electors have just spent two days locked into their pressure-cooker, the Sistine Chapel, to determine who will bear the keys of St. Peter. They were all sequestered in the Vatican, that enclave in the middle of the Eternal City, locked in debate and prayer and voting. Literally locked in: the doors of the Sistine Chapel were locked.
That is why this gathering is called a conclave: it is held in a conclave. The place it is held is a conclave because it is locked. Here is the key to this word: con 'together' and clavis 'key.' There's that clasping coarticulation of the /kl/ — so good for occluded and occluding things: clasps, clutches, cloaks, closets of clothes, clouds, cloisters, cliques and clubs (but also clergy and clemency and many other less closed words). We see the clave root in other words too: autoclave, a high-heat, high-pressure cooker or sterilizer — from French marmite autoclave, 'self-locking pot' (if you own a pressure cooker, you get the picture); enclave, a territory locked in (surrounded) by other territories; clavicle, the collar bone — over which papal regalia may be draped, such as the keys of St. Peter.
Those keys, yes. They're on the flag of the Vatican and in assorted other papal places. Did St. Peter carry those keys? No, they symbolize what Jesus said to Peter in Matthew 16:19: "I will give you the keys of the kingdom of heaven, and whatever you bind on earth will be bound in heaven, and whatever you loose on earth will be loosed in heaven." It is perhaps fitting, then, that once a new pope is elected, the doors of the conclave are unlocked, opening once again to public view the vision of heaven painted on its ceiling by Michelangelo.
But first, for two days, the cardinals were locked in and the subordinates were locked out — as were the assembled hordes of newspeople outside (keeping their distance so their cell phones worked — there were mobile phone jammers under the floor of the Sistine Chapel, preventing any cardinal from live-tweeting the event), who had to key in nothing more than bootless (and red-shoe-less) guesses. They might as well have been standing above the Large Hadron Collider while it's busy smashing atoms. Nothing is known during; only the result is revealed: God particle or God partisan, as the case may be.