In astronomy dark matter is a type of matter speculated to be responsible for huge parts of the universe. We can use physics and mathematics to understand how strongly gravity affects something if we know enough about that thing, mainly how much mass it has. This way, we can understand how objects act on Earth.
However, astrophysicists have learned that the way things in deep space behave is different.
Many scientists have tried to understand why the rules are different in deep space. One idea is that we do not really understand gravity as well as we think we do. Another idea, which many think is more likely, is that there is something called 'dark matter'. If you do calculations on the things in deep space with extra mass, then the rules work there too. So the idea is that there is more matter - stuff - in the universe than we thought. This is called dark matter because we can not see it, but if we assume the rules are right then it must exist.
Because dark matter does not seem to give off or reflect light, x-rays, or any other radiation, the instruments which can find normal matter (like hot gas, stars, planets, and us) are unable to find dark matter. It seems that dark matter is not made of the same thing as the matter we see everyday on Earth. The only way we can tell it is there is by how it affects things we can see by gravity.
In 2006, a group of scientists claimed they had found a way to observe dark matter. Since dark matter is supposedly very different from normal matter, it is expected to act differently. They observed two galaxy clusters that had crashed into each other at high speed: normal matter would have got stuck behind after the collision, while dark matter would not. By measuring gravity they were able to detect what looks like two clouds of dark matter, with a cloud of normal matter (hot gas) in between them.