To expand on this, people will commonly give you unintentional "hooks" for where you can go to increase the depth of the conversation.

For example, people use common words as short hand for many things ("Work was stressful", "The kids are being a pain", "We had a really nice weekend"), and a mistake people run into when talking with others is that they assume the person they are talking with meant they same thing they themselves would have if they had used that phrase. This leads to lots of people "listening but not understanding".

So basically, offhand comments and common phrases are a great place to get a person to dig in deeper into their feelings on a topic. Usually they indicate something that is on the person's mind but that they probably haven't worked through enough to put into words. That means you will get a much more raw and unfiltered response from them.

Also it's always good to remember that people love to talk about themselves, even if they say they don't.