If there's one question that is my most favorite to answer, it's the very simple "How do we know?" Explaining cool facts about the universe is always fun, but getting a chance to share how science is done, beyond the overly-simplified grade school "memorize the scientific method for the quiz on Friday" level, is where some really deep science communication happens.
And when we know something based on direct observation or experiment, folks are usually easily satisfied. "We know this because we made a hypothesis and tested for it" wraps up everything in a nice little easily-appreciated package. Unfortunately, most of the time it's not that simple.
Take the case of the interior of a black hole (a question I get a lot). We will never see inside a black hole, and if you were to visit one you would a) die horribly, and b) never be able to communicate your gruesome results to the outside world. So how do we know what's inside?
The answer is inference, or using reasoning and evidence to follow logical paths to make ever-more complicated statements. We can infer about the interiors of black holes because we understand the mathematics and the observations of what we can see - we don't have to actually go there to have a handle on the situation.
But what if we're wrong? Well, that's a possibility...but one that is omnipresent in science. Science is all about inference - about making provisional statements based on the accumulated evidence. The statements can always be overturned with future evidence or rational arguments. Even in the case of direct observation or experiment - which on the surface appear oh-so-comforting - inference is still the tool that we use to build our entire scientific worldview.
And while that subtlety is really hard to communicate, we can't avoid it.