Previously, we discussed the fact that 96% of the universe is made up of things we don't understand. About 22% of this we call dark matter. We think dark matter exists because we see regular objects, like stars and galaxies, interacting gravitationally with something that we can't see. The best and easiest to understand example of this comes from galactic rotation curves. Galactic rotation curves (shown below) are a graph showing how fast different parts of a galaxy spin. Here's what we expect. Think of a galaxy as a large funnel. You have a black hole at the center attracting all matter, and the rest of the galaxy extends outward in a circular fashion. If you were to take a marble and roll it along the inside of the funnel, how would the speed of the marble's rotation change? Well, you should see that the marble rolls slowly when its close to the edge, and much faster as it approaches the inside of the funnel until it falls through the central hole. We expect to see the same behavior in stars orbiting around the black hole in the center of galaxies. Stars close to the galactic center should orbit quickly, and the speed should decrease as you move away from the center. Below is a simple galactic rotation curve showing what scientists predict, and what we observe for almost all galaxies.
As you can see, stars in a galaxy all orbit the center at about the same speed! This means that your marble is rolling around the inside of the funnel at the same speed regardless of whether its at the edge or about to fall through the center! Physics states that the velocity (speed) of an object due to gravity is proportional to its mass. The only easy way to explain this is that there is lots of matter that we can't see towards the outer edges of galaxies, ergo Dark Matter! This would allow the stars at the edge of the galaxy to orbit at the same rate as the ones near the center.
Of course there is always the possibility that our science or math is incorrect, and the theory of gravity needs to be modified. Some scientists are working on that idea, but dark matter is still the winning hypothesis.