When I was a kid an astrophysicist in my family explained black holes to me using a simplified model like this.

Imagine the fabric of space-time as a literal fabric, a trampoline. When you put a heavy object like a planet, or a bowling ball onto that trampoline it warps and distorts the shape of the surface. You can see how other objects will be attracted to that heavy object, how two heavy objects might be attracted to each other, and to some degree how an object might orbit around that heavy object, like one of those spinning coin funnels. If we imagine that bowling ball being much heavier, much denser, we can imagine how it will distort the fabric more and more, making its effect on other objects more dramatic, until eventually it is so dense and heavy that it tears through the fabric of that trampoline. Unlike the trampoline though, the fabric of space-time won't spring back when the ball tears through, and that heavy hole in the middle of the trampoline will continue to very dramatically affect other objects.

So it isn't that it has infinite density, but that it doesn't matter if it's denser than the point at which it tears a hole, it's still going to tear the hole either way. So it's more like the "speed limit" of density.

I'm not sure exactly how accurate that is, but to an 8-year-old Emma it made sense and was a lot less scary than the perception that black holes were some sort of a "glitch in The Matrix"