You find parallelism between two things that are alike, like parallel lines. If your path in life is to save the world from an evil wizard, you can remark on the parallelism between your life and Harry Potter's.
In English grammar, parallelism is used in sentence construction to give matching structure. In the sentence, "I like to read, dancing, and fighting off Zombie attacks," the parts of the list are not parallel. You can revise the sentence for parallelism: "I like to read, to dance, and to fight off Zombie attacks." Of course, if Zombies are attacking, they probably don't care if the sentence parts are parallel or not.