To attack a person’s reputation and views.
The term was popularized by the Wall Street Journal editorial page after the Senate rejected the nomination of Robert Bork the U.S. Supreme Court in 1987.
Bork himself later discussed the origination of the term in a 2005 interview with Frank Sesno on CNN:
BORK: Well, I knew what was happening. The core of the issue was, they were afraid I would vote to overrule Roe against Wade. And they were quite right.
SESNO: And your name became a verb.
BORK: My name became a verb. And I regard that as one form of immortality.
SESNO: To Bork means what?
BORK: I think to attack with — to attack a person’s reputation and views unfairly.