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
Doctor Strange and America Chavez travel to another universe called 838 and hope to come across another version of himself to help them get back to earth 616. They come to 838's version of the New York Sanctum and Baron Mordo - an alternate version of Karl Mordo - who greets the duo warmly, much to Strange's dismay and confusion.
Inside the sanctum, Mordo informs Stephen and America about Strange's alternate self who was the Sorcerer Supreme of that universe before his death. Mordo explains that 838 Doctor Strange was the leader of the Illuminati (838's version of the Avengers), until he began to take possession of the Darkhold and began to dream walk, causing an incursion. Unknown to Strange and Chavez, Baron betrays and drugs them to knock them out, and they are taken to a felicity where they meet another Christine Palmer. Baron comes in and tells Doctor Strange that he must meet the Illuminati, which Mordo is apart of.
With the Illuminati, Mordo informs Stephen of how dangerous their version of Doctor Strange was, saying 838 Strange was a bigger threat than the Scarlet Witch. When the Illuminati go to confront Scarlet Witch, Mordo fights 616 Strange, who defeats Mordo. With Strange running off, Baron says he can see why the 616 version of himself did not like Doctor Strange. He is also the only member of the Illuminati who survives Scarlet Witch's massacre at the headquarters.
It is unknown what exactly happened to the Karl from earth-616, but Strange does mention to America Chavez that Mordo dedicated his life to try and kill Strange, which he failed to do.
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.