In the books, Jason Bourne is a Treadstone operative, which is a black ops division of the CIA. He was known as David Webb, who was a military man as well as a scholar specialising in the culture and languages of East Asia.
It is revealed in the books that his wife and child are killed by a stray fighter aircraft of indeterminate military affiliation. The grief and rage from this loss drive Webb to join the Medusa Company. Medusa Company was made up of hardened criminals who were serving life long prison sentences or facing execution. They were offered a clean slate if they joined this company. No one in the company went by their real names. Medusa Company was sent to near suicide missions repeatedly in Nam, lead by David Webb who assumed the name of "Delta". As Delta, David Webb ruled Medusa Company with an iron fist inspiring fear and dread in his colleagues and the enemy combatants.
A man called Jason Bourne, who was simply a radio communication expert also in trouble with the law, was placed in this company. He later betrayed the location of Medusa Company while in hostile territory through his aforementioned skills. Delta executed him in the jungles of Nam when he learned of his betrayal.
After the war was over, David Webb aka Delta still seething with rage needed an enemy to fight. He was recruited by Treadstone where he was trained for the purpose of capturing or killing an infamous assassin named "The Jackal". David Webb then assumed the name of Jason Bourne and became "Cain the Assassin". He traveled to East Asia and quickly gained a fearful reputation using the Jackal's tactics. He then moved to Europe to challenge the Jackal as planned. The Jackal bought the bait and came after Cain. But before David Webb aka Delta aka Jason Bourne aka Cain could complete his mission, he was injured which resulted in him losing his memory.
The adaptation of the book series to the silver screen ended up altering Bourne's origin story. Here he is a Treadstone operative sent to kill Wombosi, a Nigerian politician. He is a trigger-pull away from succeeding before seeing a child looking up at him, and walks away. Bourne is then shot in the back by Wombosi's men and falls over a railing into the Mediterranean Sea, where he loses his memory.