Elmore Leonard likes to start scenes right in the middle of the scene, as he does, more or less, in the scene above from Steven Soderbergh's "Out of Sight," adapted from Leonard's novel of the same title. At too many Daves, David Quigg considers the virtue of starting an entire book in its middle:
Actually Quigg is considering there a book that talks of starting books in the middle; that larger passage, starting with "I turned..." is from a novel Quigg is reading called Rules of Civility, by Amor Towles; the passage in italics is from Hemingway's To Have or Have Not. Quigg has a wonderful riff on the Hemingway passage, which he quickly found in yet another book; do check it out.
I suspect the fun of starting in the middle — of being dropped into the middle — derives from being forced to rapidly create, in your mind as you read, a lot of context. It's the fun of the jumpcut or, from real life, of walking into a room and finding two people in a conversation so heated or otherwise committed that they don't stop to fill you in; instead, you have to fill the scene in. You become a creator.
PS: One reason I like this scene so much is that Clooney's ploy here depends, quite perversely, on getting that teller to trust him: to believe his improvised story that the man at the table is his compatriot. "Trust me, I'm a bank robber," is an odd thing to ask of someone, but it works. So the teller of the tale makes an accomplice of the teller of the bank.
PPS: A few hours after I ran the above, David Quigg, who posted the excerpted excerpt that started this, threw the ball back from over at too many Daves:
When I'm finished shaking the sting out of my catching hand, I'm sending one back Quigg's way. Stay tuned.