At some point in his life, Karl suffered a great loss and visited Karma Taj, where he learnt the abilities and magic from the Ancient One. He wanted to learn magic and the abilities to avenge the life of the loved one, although he was known to be disrespectful to those around him. However, when he was being trained by the Ancient One, he dedicated his life to becoming a master and put aside his desire to get revenge, becoming friendly with Wong. He and Wong became good friends and worked side-by-side, although Wong became worried about Karl's beliefs.
Role in the film
Karl Mordo was a student of the Ancient One who overheard Stephen Strange asking people for directions to the Kamar-Taj. Strange was attacked by three muggers, but Mordo saved his life. Following the attack, Mordo brought Strange inside Kama-Taj to meet with the Ancient One, who taught Strange magic, alongside Mordo and Wong.
Sometime later, Mordo trained with Doctor Strange in fighting and told him that the Ancient One was trustworthy despite her secrets. Karl was informed by Stephen that the Ancient One had lied to all of Kama Taj to not find a way to stay alive for centuries, which she had been doing herself. Karl argued with Stephen about the Ancient one, believing she was trustworthy.
Following the Ancient One's death, Karl was recruited by Doctor Strange to fight the Zealots. However, during the battle and Wong was brought back to life by the Eye of Agamotto, Mordo decided to quit the Masters of the Mystic Arts and walked away. after becoming disillusioned by their dangerous use of magic.
A while later, Mordo came across Johnathan Panghorn in his factory, who asked why he was there. Mordo explained he had a revelation while he was at Kama Taj and made it clear he had quit the Masters of the Mystic Arts. Karl defeated Panghorn, who questioned Mordo's motives, to which Mordo declared his intention to cleanse the world of all of the rogue sorcerers.
Following these events. Mordo spent years hunting down Doctor Strange and vowed to kill him but failed, which Strange mentioned to America Chavez.
In the MCU, he is black-skinned, but in Ultimate Spider-Man and other cartoon appearances (as well as the comics), he is white-skinned.
It has never been fully revealed what exactly happened to Karl from the first film after he left the Masters of the Mystic Arts, although Doctor Strange does mention that Mordo dedicated his life to try and kill Strange, in which he failed.