The paradox happens when a person travels to the past and kills his grandfather before he meets his wife, who is his grandmother. In this way the existence of this person becomes impossible.
Some argue that the continuation cannot be changed. Therefore, as you travel into the past and kill your ancestor, a parallel universe would emerge. Others say that time is always the present and that by killing your grandfather your past would simply disappear, and your existence would begin the moment it appeared in the time machine.