The Grandfather Paradox is a crucial element in time travel and alternate history stories because it changed the way we see the role of cause and effect in literature and film. It is a type of temporal paradox that explores the scenario wherein you go back in time where you purposely or inadvertently kill one of your direct line ancestor like your grandfather. It also applies to anything that happens while time travelling that should logically make your original time travel trip impossible or unnecessary.
So how do you picture it out? Consider the following scenarios:
1. If you killed your grandfather in the past, you should never have been born, and therefore you couldn't have traveled to the past to kill your grandfather.
2. Destroyed the time machine? Okay, but how did you use said machine to travel into the past in the first place?
3. Kill Adolf Hitler while he's a child? Then you shouldn't have any reason to travel into the past to kill him, because he never grew up to destroy your village and kill so many people.
At the end of the day, when you kill your grandfather, it causes you to not exist. Since you don't exist, therefor you never killed him. Which means he survives, so you exist, so you do go back to kill him. Which means he doesn't, so you don't; therefore he does, so you do. Confusing isn't it?
But what if your grandfather does the unthinkable and kills you first before you do? Now that's interesting.
Killing someone in the past is basically mass murder of people that are offsprings of that person.