This is one of the most famous lines from the film, and the film's first statement of the idea that what we do in life can ensure that our memory lives on.
MARCUS AURELIUS: When a man sees his end he wants to know there was some purpose to his life.
Marcus Aurelius' comments to Maximus pick up the same theme—the survival of our deeds after the death of our bodies. He wants to know "there was some purpose" because he wants to be remembered after death (which is just around the corner) for doing good, not for waging war and other things.
PROXIMO: I did not pay good money for you for your company. I paid it so that I could profit from your death.
For Proximo, death is a business. For him, life only has value insofar as it has a monetary value. There may be a tiny bit of foreshadowing here. While Proximo doesn't profit from the deaths of his latest batch of gladiators, Rome will eventually profit from Maximus' death (they will be rid of an evil emperor).
PROXIMO: Ultimately, we're all dead men. Sadly we cannot choose how, but we can decide how we meet that end in order that we are remembered as men.
This is Proximo's take on Maximus' idea of our actions echoing in eternity, and Marcus Aurelius' ideas about life having a purpose. For Proximo, being "remembered as men" is the equivalent of becoming immortal. To be remembered as a man, one must fight boldly and heroically…which Maximus does.
MAXIMUS: My name is Maximus Decimus Meridius, commander of the armies of the north, general of the Felix legions, loyal servant to the true emperor, Marcus Aurelius, father to a murdered son, husband to a murdered wife, and I will have my vengeance, in this life or the next.
Maximus' life is really more like a death. Death is all around him. All the people he names in this statement of his identity—Marcus Aurelius; his wife and son—have been cruelly murdered.
PROXIMO: We mortals are but shadows and dust.
Proximo loves life, and he loves making money, but he knows that in the end we're all just mortals. We started as shadows and dust, and become shadows and dust at the end. Or do we? Maximus goes to the afterlife. His body may return to "dust" but his spirit journeys on.
MAXIMUS: I knew a man who once said, "Death smiles at us all." All a man can do is smile back.
Maximus never once acts as though he's afraid of death. He's internalized the words of Marcus Aurelius (which he quotes here), and knows that death will come when it will come. There's no way around it. That is one of the reasons he is so fearless.
LUCILLA: Is Rome worth the life of one good man? We believed it once. Make us believe it again. He was a soldier of Rome. Honor him.
Maximus' death, while tragic, proves to be heroic and meaningful. His life is sacrificed, essentially, for Rome. Commodus' death also, strangely, saves Rome as well, but there's nothing sacrificial or heroic about it, just as there is nothing sacrificial or heroic about killing of a virus.