The truth Morpheus refers to is that the world Neo believes in is just an illusion. What Neo perceives as real by his senses is nothing more than a computer generating ideas in his head without any real experiences. Morpheus gives Neo the option of continuing to live his life in the shadows and the way he perceives it or to see the light and the truth. This closely resembles the allegory of the cave by Pluto. Plato invites us to imagine humans being held prisoners, with no freedom to move or see except what is directly in front of them in the form of shadows. This is the prisoners reality.
This is what they come to believe is real. When in-fact there is another world just beyond their reality. It is only after one prisoner escapes the shackles and chains and finds that the actual world is not just shadows but a world with the light of the sun. The prisoner has difficulty adjusting his eyes to the brightness, but eventually does. This experience parallels to what Neo experiences. Descartes poses the questions in his work Meditations of First Philosophy, 1961, of how we cannot for certain that the world he experiences isnt not the product of an illusion forced upon him by an evil demon.
He questions what he believes is real because of what he sees and feels while dreaming and therefore cant trust his senses to tell him if 2he is still dreaming. When Neo accepts the red pill and his perception of his life slips away when he realizes that the human race is held in containers, unconscious, with a computer generating their thoughts and experiences. Humans invented Artificial Intelligence and in turn the AI took over mankind and enslaved them using them for the energy they required to stay alive.
Neo realizes what Descartes proposed, that Neos life was just controlled by an evil demon, the Matrix. But Descartes went on to argue the existence of God, saying a Good God would not let an evil demon control us. Neo struggles with this new truth because he didnt believe in fate because he didnt like the idea he wasnt in control of life. Neo life as he knew it is gone, and he is faced with the new reality and he struggles with the different emotions first of shock, fear and disbelief and then acceptance.
He joins the group of dissidents to help others see the truth and reality of life. Knowing the truth doesnt necessarily set you free as we find out. A fellow dissident Cypher discovers the truth is hard and decides that ignorance is bliss. He negotiates a deal to deliver Morpheus in turn for his previous life. For Cypher, the truth was too much to handle, he liked the illusion of his previous life. Once Neo gains knowledge of he Matrix, he is able to discern between the truth and illusion and ascends to a higher level of understanding.
He realizes that he can no longer blindly accept information received through his senses, but must requires answers to his questions. He like Descartes comes to the conclusion I think, therefore I am. The difference between the Matrix and Plato and Descartes is the movie gives Neo a way back to the physical real world whereas Plato and Descartes only suggest there is another reality and we are dreaming but doesnt give us a way back. None of the notables address God within the realm of truth. God states he is the way of the light and the truth. We are challenged in our daily lives to live a real life.