Carl Zimmer profiles astrophysicist Neil deGrasse Tyson. Here's Tyson explaining the problem of dark matter to a young boy:
[E]verything we've ever seen in the universe has gravity–Earth, the moon. And you can tell how much gravity something has by how fast something moves around it. … Add it all up. We've done this. Add it all up and say that should give me this much gravity. But when you look at how fast things are moving, you get six times as much gravity as the stuff that we know about is generating. It was originally called the missing matter problem. Where is the matter that's making this gravity that we see? Because everything we do count up doesn't get us where we need. We now call this the dark matter problem.
But really we have no idea what's causing it. We so don't know what's causing it that we shouldn't even call it dark matter because that implies we have some understanding that it's matter. We don't know what it is. I could call it Fred. Eighty five percent all the gravity in the universe comes from something about which we know nothing. …
[Add that to dark energy and] it is ninety six percent of the universe. Everything we know and love–electrons, protons, neutrons, light, black holes, planets, stars, everything we know and understand–occupies four percent of the universe. Dark matter and dark energy is everything else.
("Cluster Crash Illuminates Dark Matter Conundrum" from NASA)