Cain in The Bourne Identity is the alias Webb adopts when he's pretending to be the up-and-coming assassin trying to steal Carlos's business. The word "Cain" was, the novel says, the word soldiers used to indicate the letter "C" during Vietnam, since "Charlie" referred to the Viet Cong. So"Cain" stands for "Charlie"—and "Charles" is also the English for "Carlos." Cain is an equivalent (or identity—see "What's Up With the Title?" for more) for Carlos. It's a warning to Carlos that Cain is going to replace him.
There's another possible meaning for the name, though. Cain is a Biblical figure: he's the son of Adam and Eve. Cain kills his brother, Abel, in Genesis 4. After killing Abel, God curses Cain, making it so that nothing he plants will ever grow. Cain worries that everyone will despise him and that "every one that finds me shall slay me." But God instead puts a "mark" on him, so that all the world will know that he is under protection, and that he is not to be harmed.
Now, the connection between the Biblical Cain and Bourne is a little confused. When Bourne in the novel refers to the "stigma of Cain" (17.236), that stigma (the fact that he's an assassin, he thinks) is why everyone's out to get him. In the Bible, the mark of Cain is a symbol that's supposed to prevent people from harming him; for Bourne, the mark of Cain is something that makes people want to harm him.
But, as we mention in our "Symbol: Eyes" section, The Bourne Identity isn't all that worried about symbols in the first place. When you're rushing pell-mell through 600 action packed pages, you're not really pausing to check and make sure your Biblical references make complete sense. Biblical Cain is a murderer; Bourne is (supposedly) an assassin—and, more importantly, one who (people believe) has killed his brother, Gordon Webb.
People want to kill Cain; people want to kill Bourne. Cain's an outcast; Bourne is an outcast. That's all the novel is trying to get across—and even if "Cain" as a symbol doesn't work perfectly, it works well enough.