In 1991 Los Angeles, slacker Jeff "the Dude" Lebowski (Jeff Bridges) is assaulted in his home by two hired goons (Mark Pellegrino and Philip Moon) who demand money that the wife of a Jeffrey Lebowski owes to a man named Jackie Treehorn (Ben Gazzara). The two soon realize they have attacked the wrong Jeffrey Lebowski and leave, but not before one of them urinates on the Dude's rug.
The Dude meets his bowling friends, the timid Donny (Steve Buscemi) and the temperamental Vietnam veteran Walter Sobchak (John Goodman). Encouraged by Walter, the Dude approaches the other Jeffrey Lebowski (David Huddleston), the eponymous "Big Lebowski", a cantankerous elderly wheelchair-bound millionaire, to seek compensation for his ruined rug. Though his request is promptly refused, he craftily steals one of Lebowski's rugs by telling Brandt (Philip Seymour Hoffman), Lebowski's sycophantic assistant, that his boss told him to take any rug in the house. The Dude subsequently meets Bunny (Tara Reid), Lebowski's young nymphomaniacal trophy wife.
Days later, Lebowski contacts the Dude stating that Bunny has been kidnapped. Lebowski wants the Dude to deliver a briefcase containing a million-dollar ransom and see if he can recognize the culprits. Later, a different pair of thugs appear in the Dude's apartment, knock him unconscious, and take Lebowski's rug. When Bunny's kidnappers call to arrange delivery of the ransom, Walter suggests they give the kidnappers a ringer instead, namely a briefcase filled with dirty underwear laundry. The kidnappers grab the ringer and leave. Later that night, the Dude's car is stolen, with the real ransom briefcase still inside.
Jeffrey Lebowski's daughter Maude (Julianne Moore) contacts the Dude and reveals she took the rug, explaining that Bunny is one of Jackie Treehorn's porn stars. She reckons that Bunny "kidnapped" herself and asks the Dude to recover the ransom which Lebowski illegally withdrew from the family's foundation. Lebowski is angry that the Dude failed to deliver the ransom and shows him a severed green-painted toe, allegedly belonging to Bunny, delivered by the kidnappers. Later, a gang of German nihilists (Peter Stormare, Torsten Voges, and Flea) invade the Dude's apartment and threaten him, identifying themselves as the kidnappers. Maude says the German nihilists are actually Bunny's friends.
The Dude's car is found by the police without the ransom money, and he reclaims it. Later, while cruising around in the car, The Dude finds the homework assignment of a high school student named Larry inside. Taking this to mean that Larry was the one who stole the car, Walter and The Dude go to his house, believing Larry has also stolen the money. When Larry refuses to respond to Walter and the Dude's threats, Walter wrecks a new sports car parked outside which they assume Larry bought with the money. However, a neighbor rushes outside, reveals himself as having just bought the car and angrily wrecks The Dude's car in revenge, thinking it to be Walter's.
The Dude is forcibly brought before Treehorn, who asks about the whereabouts of Bunny and says he wants the money she owes him. He drugs the Dude's White Russian cocktail, leading to an unconscious dream sequence involving Maude and bowling. The Dude comes to in police custody, where he is verbally and physically assaulted by the Malibu police chief. During the cab ride home, the Dude gets thrown out after he asks the cab driver to simply change the radio station. A red sports car zooms past and the viewer sees that Bunny is driving, with all her toes intact.
The Dude finds his bungalow completely trashed and is greeted by Maude, who seduces him. He figures that Treehorn drugged him so that his goons could look for the ransom money at the Dude's home. After Maude has sex with him, she says she hopes to conceive a child; the Dude is about to protest the idea of being a father but Maude tells him that he doesn't have to have a hand in the child's upbringing. Maude also explains that her father has no money: her mother was the wealthy one and she left her money exclusively to the family charity. The Dude later tells Walter that he now understands the whole story: when Lebowskiâwho apparently hated his wifeâheard that Bunny was kidnapped, he withdrew money from the foundation, kept it for himself, and gave the Dude a briefcase without any money in it, saying that it contained a million dollar ransom. The kidnapping was also a ruse: when Bunny took an unannounced trip, her friends (the nihilists) faked a kidnapping to be able to extort money from Lebowski. Walter and the Dude confront the Big Lebowski, who refuses to admit responsibility, but is thrown out of his wheelchair by Walter, who believes that he's faking his paralysis.
The affair apparently over, the Dude and his bowling teammates return to the bowling alley. When they leave, they are confronted in the parking lot by the nihilists who have set the Dude's car on fire. They, once again, demand the ransom money. After hearing what the Dude and Walter know, the nihilists try to mug them anyway. Walter violently overcomes all three, biting the ear off one of them. However, in the excitement, Donny suffers a fatal heart attack.
Walter and the Dude go to the beach to scatter Donny's ashes. Walter turns an informal eulogy into a tribute to the Vietnam War. After accidentally covering the Dude with Donny's ashes, and after a brief argument, Walter hugs him and says, "Come on, Dude. Fuck it, man. Let's go bowling." At the bowling alley, the story's narrator (Sam Elliott) tells the viewer that Maude is pregnant with a "little Lebowski" and expresses his hope that the Dude and Walter will win the bowling tournament.

Question: Why did Jeffrey's daughter take the rug? 
Answer: Bunny is one of Jackie's porn stars. 
Alternative answer: She thinks Bunny is faking the kidnapping for the ransom money.