The 'elevator pitch' is where you're outlining your idea in brief so you can pose it to someone in the course of a one-two minute elevator ride (ie, an editor, producer, whatever). I spent a while honing mine, so I'd have my mental footing if people asked about the story.
Good elevator pitches will use the same technique that a news segment (be it TV or newspaper or radio) will. In short, you start with something broad that encompasses the idea of the story, then give more detail. The specifics only come up in the end, assuming you have your audience's attention with the early stuff.
You have to avoid being nonspecific, and in reviewing others' elevator pitches, I noticed that there's a few errors that recur:
The last time Solomon Calibre slept, he woke to find a pocket watch under his pillow engraved with a mysterious message: The world is winding down.
The engraving is true.
Crops are failing. Mutated crustaceans the size of bulls stalk the scrub lands sniffing out prey. Entire villages disappear over night. And Solomon hasn't slept for years. What priests and thinkers are left have no explanation, but Solomon thinks one man does.
For three sleepless years he has chased the clockmaker across the dying kingdom of Herthule. Now on the cusp of catching up to his obsession, he'll learn what he would sacrifice for answers.
This is more of a premise than a pitch. Something you'd see on the back of a book. The thing about the synopsis you'll see on the book jacket is that a lot of -other- information is already conveyed. The cover, the font, the layout, they convey the attitude and tone. That's stuff you have to convey
And note the final sentence. It's vague, and it doesn't convey the nature of the story, and it's vague, nonspecific when you want the opposite. Is it a story of transformation? A tragedy? A comedy? The last one would be a stretch, but it's there.
What they will discover has greater implications than they ever could have imagined.
And are we making our robots more human than ourselves?
Human civilization will never be the same.
Will the ties of friendship, love, and duty prove the way, or will the easy power of cruelty and dominion be too hard to resist?
Probably the former.
These are lines to avoid, all too common closing sentences when you're trying to do a pitch. The first quote above sort of makes the same mistake, to a lesser degree.
Don't frame the central question, and definitely don't frame it like that. A binary question is problematic, because the reader can guess. It should point to a world of possibilities without being vague.
What I'd say would be something like...
The Parity II's crew found hints of an ancient genocide of an entire race, with a cover-up spanning multiple star systems. With entire planetary governments now intent on eliminating them before they can leak the information, the crew is caught between a need to gather usable evidence and their desire to seize the narrowing window to home. With every passing hour, frictions within the ship intensify and assassins, mercenaries, armies and traps gather between them and their unlikely asylum.
Mayor of an isolated city-colony, Haukner struggles against a terrorism campaign led by reformist androids. They are immortal opponents smarter, stronger, with better scientific and artistic minds than the colonists working under him, and they want nothing more than to supplant him. With no human connections but his sham of a marriage and a daughter who loathes him, Haukner finds himself caught up in his affair with the android Else94. It would be everything he dreamed of, if he didn't find himself wondering if she were a succubus, manipulating him into his downfall. With the city-colony in his hands, he has to fight, manipulate and lead his way through the crisis, no matter which side he ends up supporting.
That's a little more than a closing line, but I'm sort of folding the whole pitch into those.
Once you get familiar with your elevator pitch, though, I think it's easier to present the idea. Bonus is, if you take the 'more general to more specific' route, you can key just how much information you provide, depending on the interest shown. If they aren't keen, then you stop partway, and you've still encapsulated most of the story.