Morpheus is the name of a fictional character (played by Laurence Fishburne) in the science fiction film, The Matrix.
Formerly plugged into the Matrix, he is now the captain of the Nebuchadnezzar (a ship in the real world). When he went to visit the Oracle, she told him that he would be the person who would find the One. Since then he spent his life searching the Matrix for him. Morpheus is apparently a very famous public figure in the city of Zion. He is also known in the Matrix, but as a dangerous terrorist.
It was Morpheus who took the risk of helping Neo escape the Matrix despite being over the maximum age at which a mind can be freed, because he knew Neo to be the One.
In the early drafts of The Matrix screenplay, one revelation during the story was that before meeting Neo, Morpheus had believed five other people to be the One, all of whom had died at the hands of Agents after being freed. This aspect of Morpheus's history was dropped, although the notion of five Ones before Neo was reused in The Matrix Reloaded.
The Wachowski brothers, writers and directors of The Matrix films, were fans of Neil Gaiman and based the character of Morpheus on the title character from the comic book The Sandman, also adopting one of his most common pseudonyms, Morpheus. They gave Fishburne some or all of the series to read, and the style of speech and mannerism of the Matrix character are heavily informed by the Sandman character, although since The Sandman is only a graphic novel, much of the tone and inflection is an original (though recognizable) interpretative creation on Fishburne's part. This connection is hinted at again in Enter the Matrix when Niobe calls Daniels Institute of dreams to get in touch with Morpheus.
The name of Morpheus actually has a reference to classical mythology. In Ancient Greek Mythology, Morpheus was the god of dreams.
