Morpheus is the captain of the Nebuchadnezzar, which is a hovercraft of the human forces of the last human city, Zion, in a devastated world where most humans are grown by sentient machines and kept imprisoned in the Matrix, a virtual computer-generated world. Morpheus was once a human living inside the Matrix until he was freed earlier in life by the "One" before Neo.

Morpheus is apparently a very popular public figure in the city of Zion. He is also known in the Matrix, but as a dangerous terrorist wanted by 'Agents', who appear to be Federal investigators but are sentient computer programs that patrol the Matrix, eliminating any threat to the Matrix.

Like other hovercraft crews, Morpheus and his crew are dedicated to the protection of Zion and the freeing of humans from the Matrix.

The name Morpheus is that of the god of dreams in Greek mythology, which is consistent with the character's involvement with the "dreaming" of the Matrix. The mythical Morpheus and his family, including two brothers (Phobetor and Phantasos), lived in a dream world protected by the Gates of Morpheus with two monsters standing guard. Beyond the gates were the River of Forgetfulness, beside which Morpheus once carried his father to hide in a cave, and the River of Oblivion. This theme of duality carries over to Morpheus in The Matrix, who offers Neo either a blue pill (to forget about The Matrix and continue to live in the world of illusion) or a red pill (to enter the painful world of reality).