Dark matter is a mysterious form of matter which exerts gravitational effects on ordinary matter but cannot be observed via any other means. While conventional matter-clouds can be detected through their stellar activity, light scattering, radio emissions, and other means, dark matter clouds are invisible to the vast majority of our instruments. Yet they constitute 90% - 99% of the matter in the universe.
In the 30s, astronomers Fritz Zwicky and Sinclair Smith performed an analysis of the velocity of galaxies within the large galactic clusters Virgo and Coma. They discovered that all galaxies were moving between ten and a hundred times faster than they should be, given the estimates based on observed stellar density. Something unseen was generating additional gravity.
Although Zwicky and Smith's initial observations seemed to provide strong evidence for dark matter, not all cosmologists were convinced. Because these galactic clusters were so far away, it was hard to accurately measure the independent velocities of each galaxy on a timescale of mere decades. Stronger evidence came in the 70s when scientists such as Rubin, Freeman, and Peebles began to analyze the rotation curves of galaxies. Stars in spiral galaxies, such as our very own, were moving faster around the galactic core than their observable mass would indicate.
It was eventually discovered that all galaxies contain dark matter halos that stretch far beyond the bounds of the galaxy indicated through a telescope. These halos are said to be made up of MACHOs (Massive Astrophysical Compact Halo Objects), and WIMPs (Weakly Interacting Massive Particles). MACHOs are theorized to mostly be black holes and brown dwarfs (burnt-out stars). They are made up of conventional, or baryonic matter - the atoms we are familiar with, only highly compressed. WIMPs are said to be non-baryonic forms of matter, weakly interacting particles which move at relativistic speeds. The most likely candidate for WIMPs are the neutrino and its cousins.