Characterization is the direct and indirect description of a character. Direct characterization occurs when the narrator of a story tells us precise details of the character, both physical and psychological.
Indirect characterization is what the audience infers from a character based on the reactions that a character displays as a result of different situations.
In movies there is hardly any narration, so the audience immediately builds the bond with the character after watching it, creating the indirect characterization themselves.
According to the screenplay, the characterization of Maximus is that of a soldier, son of a good friend of Marcus Aurelius, and born in Hispania in 152 A.D. He was a Standard Bearer in the military at age 17, and moved from optio to centurion, to Primus Plius.
Maximus characterizes himself in the movie with the lines:
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.
While there is no direct characterization in terms of the physical traits of Maximus, a bust found in the Tiber river in the 18th century may have been used to inspire the looks of Maximus in the movie, but that is unlikely as actors are often chosen prior to production.
Indirectly, we can characterize Maximus as the embodiment of the Roman virtues. His distinction in battle, as a husband, as a father, and as a citizen basically imply that he is a whole man, one who is well-rounded and capable of a multitude of things. So great is his capacity that the emperor even bypassed his own bloodline to favor Maximus as his heir. That he is courageous and strong is no doubt; that he is also unafraid, an gifted is also a fact. If you review the Via Romana, or the Roman Way, Maximus posesses every single factor that delineates the true Roman citizen; one who is unimpeachable and whose depth of character is incorruptible.