Morpheus is the captain of the hovercraft Nebuchadnezzar and the biggest believer of the prophecy of The Oracle. Morpheus, believing that he is destined to find "The One" that will bring an end to the war between humans and machines and the destruction of The Matrix, frees the mind of Neo and begins his journey to do just that.
Previously romantically involved with Niobe, Morpheus went on to live a very priest-like lifestyle. After the events of The Matrix films (as depicted in The Matrix: Path of Neo) and Enter The Matrix, Morpheus played a key role in the continuing existence of The Matrix and Mega City in the ongoing and tense armistice between the humans and machines (as seen in The Matrix: Online.) Morpheus was a strong proponent for returning the remains of Neo to the humans, eventually enacting attacks throughout the Matrix designed to force awakenings across the city.
As a way of silencing him, Morpheus was supposedly killed by The Assassin, although it remains a point of debate whether Morpheus was killed or merely disrupted, preventing him from returning to the Matrix. As well, this event as a whole is a point of debate, due to only happening within The Matrix: Online, leaving the potential for it to be seen as non-canonical. Morpheus reappeared later in the story of The Matrix: Online as an RSI (Residual Self Image), supposedly controlled by The General in an attempt to agitate relations between the Matrix's various factions.