Since Arda, the world, was Marred by the evil of Melkor, all things living upon it have an element of corruption. This element was generally referred to as the Shadow by the Free Peoples, but the term darkness was also used. Generally, this word more specifically referred to the shroud of ignorance and misunderstanding made by the Marring of Arda that keeps the Children of Ilúvatar from perceiving truth; just as literal darkness prevents one from seeing clearly. When used this way, darkness usually stands in opposition to the Light of Valinor. For example, when Túrin spoke against the Valar during a council in Nargothrond, the Elf Gwindor chastised him and said that "a darkness was on" him because he harbored such incorrect thoughts about the Powers.
Role in the History of Men
More specifically, the Darkness, also called the Ancient Darkness or simply the Dark, was a concept that Melkor and Sauron used with terrible effect in their attempts to seduce populations of Men. They utilized the mysterious nature of Darkness, and the fear that came from it, in coaxing Men to depend upon their teachings.
It was said that Men were seduced by Melkor in the beginning of their history, and that a residual darkness lay upon the hearts of all their race, even those of the Edain who met the Eldar in the First Age. Ancient tales that the Wise among the Edain kept told of how Melkor had achieved his mastery over their race: he came among them as a fair-seeming teacher and told them many things about the world, but increasingly he spoke about the Dark. He told the first Men that "Greatest of all is the Dark, for It has no bounds. I came out of the Dark, but I am Its master... I will protect you from the Dark, which else would devour you."