The Brainspawn invades and destroys planets by going there and using their powers to make everyone extremely stupid, allowing the brains to wipe them out easily.
According to the prophecy of the Nibblonians, the only one who can stop the brains is Philip J. Fry, who is the only being in the universe who, due to a strange anomaly in his system, lacks the "Delta Brainwave", which is what allows the brains to subvert people's minds. When Fry learns of this, he deduces that a being obsessed with knowledge would most likely be found at the library so he goes there and sure enough, finds the Big Brain reading from textbooks to absorb their information, remarking on how the fact that the books are organized by category makes it much easier for him to do so.
When Fry finds that there is nothing available in the library capable of physically harming the brain, he starts trying to think of a way to defeat it, and finds that his thinking causes pain to the Big Brain, as it hates independent thinking, and starts reading from a book to weaken it. The Big Brain reveals that he has the power to transport himself and others into the world of any book and uses it on Fry and Leela, who then pursue the brain through Moby Dick, The Adventures of Tom Sawyer (where the Big Brain is surprisingly tricked by Tom into painting the fence for him), and Pride and Prejudice, where Fry throws Tom Sawyer's bucket of white paint over the brain, making the characters from Moby Dickattack it thinking it is a white whale (however the brain seems to be immune to harpoons). Using this as a distraction, Fry escapes the book world and attempts to kill the Big Brain by riding an electrified chandelier into it, but this fails as he completely misses his target and crashes into a bookshelf which then falls over on him, seemingly killing him. Leela starts crying over him, but it is then revealed that this is only happening in a new book Fry is writing down on the spot called "Fry Tricks the Brain", thus creating a new pocket universe that the brain and Leela are inside of. Fry writes that after killing the Fry within the story, the Big Brain left Earth forever for no reason. This makes the real brain do just that, however he mispronounces "reason" as "raisin" because Fry misspelled it that way. After he leaves, the Nibblonians kill the other brains by eating them, removing their effects from the people of Earth.