Meaning of "What is your thing?"

I've recently watched Last Week Tonight With Jon Oliver (season 2 episode 2).

It shows a clip from Fifty Shades of Grey movie, where a guy asks a girl "What is your thing?" and she responds "I don't know, books?" and the audience of the show laughs and Jon Oliver responds to it "My penis just yawned"....

I don't get it. I don't get it at all.

So I googled "What is your thing" ...and "Your thing" but couldn't get any dictionary entry.

I identified that {possessive adjective} thing is some phrase but I couldn't find any meaning to it.

I found the passage from the book but I can't still put a meaning to it...

"Were you a Girl Scout?" he asks, sculptured, sensual lips curled in amusement. Don't look at his mouth!

"Organized, group activities aren't really my thing, Mr. Grey."

He arches a brow.

"What is your thing, Anastasia?" he asks, his voice soft and his secret smile is back. I gaze at him unable to express myself. I'm on shifting tectonic plates. Try and be cool, Ana, my tortured subconscious begs on bended knee.

"Books," I whisper, but inside, my subconscious is screaming: You! You are my thing!

So... "my thing" just means something important? And why would anyone ask a question like "What is your thing?" How different is that from "What is important to you?"

Answer

Your thing is what drives, motivates, interests you most. Something you are usually good at, your main focus. Often an area of expertise, after a while.
We may assume that gorillas were Dian Fossey's "thing" and Playboy Bunnies are Hugh Hefner's "thing".

It can also be your "modus operandi", a behavioural pattern or quirk.
In this sense, Charlie Chaplin's waddling walk was "his thing". Charles Ponzi even had "his thing" named after him.