Let's talk a little bit about our galaxy. You probably know that it's a spiral galaxy, with several "arms" reaching out from a central bulge, and is shaped like a disk. Most of our galaxy's mass is centered in that central bulge, with is about 13,000 light-years from top to bottom (which is really, really big), and has a density of around 1,600 stars per cubic light-year. To put that in perspective, out where we are in the Milky Way it's only a few thousand light-years thick (which is still really big), and the stellar density is closer to 0.004 stars per cubic light-year.

Stellar count is completely accurate, which made this take a lot longer than it should have to illustrate.

You can almost think of the Milky Way as a lot like our solar system: most of the mass is concentrated in the center (like the sun), with a thin disk of mass orbiting it (the planets, the asteroid belt, the Oort cloud, etc.). In fact, the galaxy rotates as well. Our own solar system completes a circuit of the galactic center every 240 million years or so, though the average for a star system completing its circuit is a bit higher. And, much like our own solar system, based on mass distribution, the outer parts of the galaxy should rotate at a significantly slower rate than the inner parts (just like Pluto's orbit takes 247 times longer than Earth's).

It's too bad that isn't the case for the Milky Way, or really any galaxies we've observed.

This observation dates way back to the 1930's. In 1932, physicist Jan Oort noticed that stars in our galactic plane were moving much faster than they should be. A year later, Fritz Zwicky noticed the same phenomenon in this and other galaxies, and hypothesized that there must be some form of non-visible matter that makes up a majority of mass in galaxies. In the 1960's and 70's, the rotation curve of the Milky Way was more accurately measured, and the discrepancies between the predicted curve by the matter we could see, and the actual, observed rotation curve became to glaringly obvious to ignore. Physicists began searching for explanations, ranging from dust to black holes, but none of them could really fit the sheer size of the matter discrepancy. The real culprit had to be some form of matter which we simply couldn't see, and that meant that it must be some form of matter which doesn't interact at all with light.

(Quick math/physics interlude: The only real way to keep the rotation speed of the outer parts of the galaxy (or of our solar system) constant would be to add more mass (from more matter). This is conceptually similar to sticking the planets together—they'd all have to orbit at the same speed at that point. But instead of physically sticking the planets (or stars, in the galactic case) together, we'd be using the increased gravity as a kind of "glue." Here are more details)

This so-called "dark matter" wouldn't really be dark, as the name suggests, it would be invisible. In order for it to not be seen by any of our reflecting or radio telescopes, it's couldn't have any influence on any part of the electromagnetic spectrum—which is just strange and unheard of. But, despite that, all observational evidense points to dark matter composing 85% of all matter in the universe. That's absurd! That means most of the universe is made up of something we can't even see.

Keep in mind, just because we have a name for this stuff, "dark matter," doesn't mean we actually know what it is. In fact, trying to figure out what exactly dark matter may be is still a thriving field today. We can observe it's effects all over the place through gravity, but we can never really get a real "look" at it, because it can't even be seen! And the more we study it, the stranger it seems to become. Every time you think we've got the universe figured out, even remotely, just think of this, or any one of the many unsolved mysteries in physics and realize that we've still got a long way to go, and it's going to be fascinating every step of the way.