Why "Genuine Curiosity"?
The concept is this: when you're talking to people about stuff, rather than trying to connect the dots in your own mind (i.e. jump to conclusions or make assumptions), hold back a bit on that tendency and ask another open ended question. Simple, but it'll make a difference in what you learn, how open people are to you, and how much you connect with them.
For example, one of the things I practice is seeing how long I can talk with someone while only asking open-ended questions. Not in a juvenile "made you look" kind of way - just to see how much I can find out.
Some of the most useful questions I've learned for this are things like:
"Really?"
"Why'd you do that?"
"What was that like?"
"Why do you think they did that?"
"What's up with that?"
"So, what are you going to do?"
Give it a try. Ask them in an "I really want to know more" kind of way. If it feels awkward, keep trying. Personally, I find it easier in a work context, but I think it's more valuable in a personal context.
What I've found is that it starts as a novelty, but you'll end up actually becoming more curious and more interested in what people are all about. And that's not a bad thing.