he was the world's most brilliant surgeon, who was a real arrogant prick. one day he was in a car crash, and his the nerves in his hands were damaged beyond repair so he would never be a surgeon again. so he traveled the world and tried to find treatments, while bankrupting himself in the process. eventually he finds this group of monks in the mountains who are lead by their master "the ancient one". and the ancient one trains stephen, and he becomes DOCTOR STRANGE...and doctor strange kinda just fights monsters in alternate realities and protects the realm of the living. as far as his personality goes, he's basically tony stark from the movies.
A little correction there, he doesn't become "Doctor Strange" his name was Stephen Strange and he was a Doctor/Surgeon, hence the name. What he becomes is the Sorcerer supreme, kinda the most badass magician the marvel universe has.