The paradox part of the Grandfather Paradox occurs when a time traveler creates a self-contradicting scenario where effect precedes cause. In this example, if you kill your grandfather before he has kids, one of your parents is never born. Consequently, you are never born. But if you're never born, then you wouldn't exist to go back and kill your grandfather in the first place, would you? Paradox! Of course, the paradox doesn't apply just to instances of grand-patricide, but to all hypothetical situations where a time traveler goes back to prevent something from occurring. If they're successful, and the event never happens, the time traveler has no reason to go back and change something. So, they might try again and ... paradox! Whatever the traveler changes doesn't have to be intentional either; accidentally interfering with a past event can also trigger a paradox.