Early on, the name of this great forest was Greenwood the Great. For a long time, it was the home of the Silvan Elves. The name Mirkwood came to it during the Third Age, when Sauron took up residence in the Southern part of the forest, in Dol Guldur.
Mirkwood is the realm of King Thranduil, father of Prince Legolas . King Thranduil is supposed to be a Sindarin Elf, who came East, and was appointed the place of King of the Silvan Elves.
Mirkwood is mentioned in the book The Hobbit, when the Dwarves are captured by the Elves, and then held prisoners, and Bilbo helps them escape.
Learn about the Evils of mirkwood by clicking HERE. Then click on "Mirkwood."