A closed timelike curve (CTC) is a world line of a material particle in spacetime that is "closed", returning to its start point.
The existence of CTC would imply at least the theoretical possibility of time travel backwards in time.
There are physicists who believe that the CTCs which appear in certain general relativity of quantum gravity which would replace general relativity theory, an idea which Stephen Hawking has labeled the chronology protection conjecture. Other scientists note that if every closed timelike curve in a given space time passes through an event horizon, then that space time with event horizons excised would still be causally well behaved and an observer might not be able to detect any violation.
One feature of a CTC is that it opens the possibility of a worldline which is not connected to earlier times, and so the existence of events that cannot be traced to an earlier cause.