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.
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 are actually sentient programs that patrol the Matrix, eliminating any human that is a threat to the secret of the Matrix or dispatching programs that exile themselves in the Matrix to avoid their deletion).
Like other hovercraft crews, Morpheus and his crew are dedicated to the protection of Zion and the freeing of humans from the Matrix.
In fact, Morpheus is the Greek god of dreams in Greek mythology, which is consistent with the character involvement with the "dreaming" of the Matrix.
Earlier in his life, Morpheus gained the romantic attention of Niobe, another hovercraft captain. Their relationship became estranged shortly after Morpheus visited The Oracle, an ally living in the Matrix. The Oracle could foretell the future, and she told Morpheus that he would be the person who would find The One, a human with superhuman abilities within the Matrix and who could end the Human/Machine war. Since that visit, Morpheus spent much of his life searching the Matrix for The One.
In the first feature film, The Matrix, Morpheus successfully finds and monitors a pod-human named Thomas A. Anderson, a hacker who calls himself Neo. Despite a close call with Agents that capture, interrogate, and place a surveillance device on Neo, Morpheus and his crew locate Neo. Morpheus offers Neo a choice of ingesting a red pill, which will activate a trace program to locate Neo's body in the real world and allow the Nebuchadnezzar crew to extract him, or a blue pill, which will leave Neo in the Matrix to live and believe what he wants to believe. Neo takes the red pill. The Nebuchadnezzar crew is then able to eject Neo's body from the Matrix powerplant and retrieve him from the cold sewers where the machines patrol. Morpheus takes a risk in helping Neo escape the Matrix, as human minds that live too long in the Matrix may have trouble in comprehending the real world and the truth of the Matrix. Initially, Neo does experience serious denial when Morpheus explains the truth, a point for which Morpheus apologizes.
Shortly after Neo first visits the Oracle, Morpheus is captured and interrogated by Agents after a crew member, Cypher, betrays the crew, killing several members before being stopped. Since Morpheus, as a hovercraft captain, possesses access codes to the Zion mainframe computer, the surviving members of the ship's crew are about to unplug Morpheus from the Matrix without the ability to retrieve his mind or his body, a process that will kill him. However, Neo had his own foretelling from the Oracle that told him that either Morpheus or Neo would die, but that he had the choice to save himself or Morpheus. Neo and Trinity reenter the Matrix to make a daring and successful rescue of Morpheus. Neo saves Trinity from a helicopter crash, confirming Morpheus' belief that Neo is indeed The One of legend.
Neo is eventually killed by Agent Smith shortly after the rescue, but reawakened as The One and returned to the Nebuchadnezzar before Sentinels can destroy the ship.
In the second film, The Matrix Reloaded, Morpheus is more confident than ever that the war is nearing its end. A spiritual as well as an influential leader, Morpheus convinces one hovercraft ship to stay in the Matrix to await contact from the Oracle, despite orders from Zion for all ships to return to the city. He incurs the wrath of Jason Locke, commander of the Zion defensive forces, but Morpheus' actions are easily defended by Councillor Hamann, a member of the Zion Council, the city's ruling body.
With the aid of Trinity and Niobe, Morpheus successfully retrieves The Keymaker, an exiled program that can access many hidden areas of the Matrix, including the Source, the central Machine City mainframe computer and programming heart of the Matrix. Morpheus aids Neo in successfully entering the door to the Source before returning to the Nebuchadnezzar.
After Neo successfully enters the Source and returns from the Matrix with new information, he tells Morpheus that the Prophecy was a lie; it was another system of control that would bring The One to the Source to disseminate the programming inside Neo into the Matrix to allow a reboot, or reload of the Matrix, while Zion is destroyed and allowed to be rebuilt. The war is far from over. To make matters worse, a sudden Sentinel attack destroys the Nebuchadnezzar, further damaging Morpheus' belief in the outcome of the war. The crew is rescued by the hovercraft the Hammer commanded by Captain Roland, who joins forces with the Logos, commanded by Niobe.
In the final film The Matrix Revolutions, Morpheus is somewhat dispirited, and has problems in understanding now what may truly happen to Zion and its people. Now without a ship of his own, he and Link (the Nebuchadnezzar's Operator) reside on the hovercraft Mjolnir, commanded by Roland. Morpheus renews his conviction that Neo could still save Zion, and reawakens Neo, whose mind is trapped in a computer netherworld called Mobil Avenue after Neo stopped five Sentinels in the real world just by thought at the end of The Matrix Reloaded. With the aid of Trinity and Seraph, he rescues Neo and returns his mind to the real world.
Morpheus says farewell to Neo and Trinity a final time before they leave for the Machine City in the hovercraft Logos in a last-ditch attempt to stop the war. Morpheus aids Niobe as she flies the Mjolnir in a desperate ride back to Zion. The ship successfully stops the first onslaught of the Machine attack with the ship's electromagnetic pulse (EMP) weapon.
When the Sentinels suddenly stop a second wave of attacks, Morpheus instantly realizes that Neo is somehow fighting for them. When the Sentinels retreat after Neo successfully defeats the former Agent Smith, now a virus that threatened both man and Machine, Morpheus, and Niobe embrace in celebration as cheers arise from the Zion population, who have received a brokered peace through Neo's sacrifice. Morpheus' dream turned out to be right after all.
Of the original Nebuchadnezzar crew in The Matrix, only Morpheus survives to see freedom for Zion.
Referring back to the subjectivity of reality throughout the film trilogy, Morpheus' last lines in The Matrix Revolutions, said in disbelief as the Sentinels retreat from Zion, are "Is this real?"