“With prejudice” means a decision is final and cannot be appealed or resubmitted.
A way to remember it: “prejudice” is a way of saying “pre-judge” or “pre-judicial.” To dismiss a case “with prejudice” is to say, “I dismiss this, and I ‘prejudge’ any further attempts to litigate it.”
Also, the phrase “with prejudice” is used much more commonly than “without prejudice.” This is because the right to submitted a case is the default. The judge only needs to be explicit when they intend to eliminate this right.
Employees are sometimes “terminated with prejudice,” meaning they are fired and cannot reapply or work at the company again.
In the 1979 movie Apocalypse Now, the phrase was modified to “terminate with extreme prejudice,” which was a euphemism for killing someone. Apparently this was a term routinely used by the CIA during the Vietnam War to refer to assassinations.