The paradox manifests itself when you stretch Einstein’s general theory of relativity to its extreme limit. The theory, in principle, allows you to go back in time and visit the past. All you need to do is to take a trip through what is called wormhole, a theoretical tunnel that connects one part of the universe with another. You would emerge in a different space-time, having accomplished time travel to an event in your own past.
Consider our nearest galactic star Alpha Centauri which is 4.2 light-years away. A light beam takes that much time to reach it when traveling through ordinary space, but you could beat a light beam by taking a shortcut through a wormhole. (See diagram.) You start your journey in the year 2012 and emerge at Alpha Centauri in 1912 instead. Now for the paradox that defies logic: What if you travel much further backwards and accidentally kill your grandfather, thereby preventing yourself from ever being born on the first place? If you were never born, you could never go back in time, and so you could not kill your grandfather.
This paradox is so potent that scientists are unable to offer any rational solution. However, science fiction writers, having more inventive minds and greater freedom of imagination, have a way of circumventing such conundrums. They say that after traveling through the wormhole you emerge in a new universe where you can not encounter your grandfather — so never have a chance to gun him down. Period.
Grandfather paradox (Wikipedia)
Below is a video explaining the paradox. Note that HBA is not affiliated with creator(s) of this video.