Muramasa was a sword smith during the Muromachi period, 1300-1500 or so. Many of his blades, especially Short Swords, Tanto, and Spears are still in existence. The famous Masamune was a Kamakura era (1185-1332) sword smith, and although things are complicated slightly by leaders of his school of blade making sharing the name, despite stories to the contrary, it seems that Muramasa wasn't a student of the Masamune school.
This myth, as well as that of the magic sword, probably better translated as something like wicked (cursed?) blade, arose in the Edo period (1603-1867.) The sword used in the murder of shogun Tokugawa Ieyasu's grandfather, the blade carried by one involved in the suicide of his son, and that which inflicted a wound he himself received were all Muramasa blades, and so Ieyasu came to distrust them. It is this that appears to have spawned the reputation of Muramasa as a cursed sword smith.