At first, scientists were pretty sure something called "dark matter" existed because when they looked at the way the universe behaved, it seemed obvious that there was something there. What it was, nobody knew. And in fact, there was no evidence that it existed.
This would make sense, since the "dark" part of the name means that it didn't radiate energy or do anything else that either our senses or our sense extensions like telescopes and other instruments could detect.
More recently, some evidence for dark matter's existence has shown up because of the one thing it does have, gravity. When astronomers look at things far away, the light, radio waves, x-rays, etc. that they use to observe them is "warped" slightly by gravity of things in between us and them. When that warping happens but no source of gravity is visible, then the most likely candidate is dark matter.
So now the question is, what makes up dark matter? Everyday matter is made up of atoms and the subatomic particles which make atoms. Dark matter can't be those, because we can see them. The "guess" name for the mysterious substance's components is "Weakly Interacting Massive Particles," or WIMPs. They have mass, because they have gravity. They interact weakly, compared to regular particles, which is why they have to be detected by gravity.
But WIMPs are still a theory, until some evidence of them can be found. That's tough, because of that whole "weakly interacting" thing. So the hunt goes on.