Marcus Aurelius's only in the film for about half an hour, but his spirit looms over the entire movie. It's clear when we first meet him that he's knocking on death's door. He's old, frail, and he knows he doesn't have a lot of time left—in fact, he flat-out says:
MARCUS AURELIUS: I am dying, Maximus.
In many ways, he's a foil for Commodus, and an example of what a good emperor is. Sure, he's done his fair share of war-mongering (and it's as part of his campaign that Maximus & Co. are fighting in Germania to begin with), but Marcus Aurelius's clearly sick and tired of it all.
Throughout the film, we learn that he doesn't really believe in pointless animal sacrifices ("Save the bulls," he says to Commodus), that he ended the gladiator games in Rome, and that, most crucially, he's done with war and empire.
This is why he wants power to pass to Maximus: so he can watch over Rome until it has time to reshape itself into a republic again. He has become, over the course of his reign, a democratic-leaning fellow, and one who wants to do the right thing.
Both his head and heart are clearly in the right place—he knows that Commodus's "not a moral man," and he also freed Proximo from a life of servitude.
In addition to having some regrets about his reign, Marcus Aurelius also seems to have a few about his parenting. He admits to Commodus that his (Commodus') failures are actually Marcus Aurelius' failings as a father, and he says that he wishes Maximus had been his son, and that Lucilla had been born a boy.
Ouch. That's got to sting a bit.
While Marcus Aurelius' comments to Commodus show us an emperor that is penitent, they also hint that maybe he's a little too eager to blame himself. Everybody else around him seems to have done all right…except for that evil Commodus.