Martin, what's interesting is that there is no direct reference to the Biblical story, except in the name.
(Warning: spoilers below.)
A plot summary from Wikipaedia:
The movie focuses on four interrelated sets of situations and characters, and many events are revealed out of sequence. The following plot summary has been simplified, and thus does not reflect the exact sequence of the events on screen.
In a remote desert location in southern Morocco, Abdullah, a goatherder, buys a high-power rifle and a box of ammunition from his countryman Hassan to shoot the jackals that have been preying on his goats. Abdullah gives the rifle to his two teenage sons, Yussef and Ahmed (played by local non-professional actors Boubker Ait El Caid and Said Tarchini), and sends them out to tend the herd. Competing gently between themselves and doubtful of the rifle's purported three-kilometer range, they decide to test it out, aiming first for rocks but then for a bus carrying Western tourists on the highway below. Yussef's bullet hits the bus, injuring Susan Jones (Cate Blanchett), an American woman from San Diego who is traveling with her husband Richard Jones (Brad Pitt) on vacation. The two boys realize what has happened and flee the scene, hiding the rifle in the hills that night.
Glimpses of television news programs reveal that the US government holds the shooting to be a terrorist act and is pressuring the Moroccan government to apprehend the culprits. Having traced the rifle back to Hassan, the Moroccan police descend quickly on his house and roughly question him and his wife until they reveal that the rifle was given to him by a Japanese man, and then sold to Abdullah. The two boys see the police on the road and confess to their father what they have done. (They believe at the time that the American woman has died of her wounds.) The three flee from their house, retrieving the rifle as they go. The police corner them on the rocky slope of a hill and open fire. After his brother is hit in the leg, Yussef returns fire, striking one police officer in the shoulder. The police continue shooting, eventually fatally wounding Yussef's brother in the back. As his father rages with grief, Yussef eventually surrenders and confesses to all the crimes, begging clemency for his family and medical assistance for his brother. The police take him into custody. The family's fate is unresolved.
The movie's first plot is interspersed with scenes of Richard and Susan. They came on vacation in Morocco to get away from things and mend their own marital woes. The death of their infant third child to SIDS (this is the implied cause) has strained their marriage significantly as they struggle to communicate their frustration, guilt, and blame. It is also implied that Richard left the family for a while after the infant's death. When Susan is shot on the tour bus, Richard orders the bus driver to the nearest village with a doctor. She receives some rudimentary treatment here, enough to save her life. The other tourists wait for some time, but they eventually demand to leave, fearing the heat and more attacks from the supposedly dangerous locals. Since Susan cannot travel by bus in her condition, the couple remains behind with the bus's tour guide, Anwar, waiting transportation to a hospital (they've managed to contact the US embassy using the village's only phone). Political issues between the US and Morocco prevent quick help, but a helicopter comes at last to carry them to the hospital. It is revealed that, after 5 days in the hospital, Susan recovers and is sent home.
Simultaneously, the movie tells the story of Chieko Wataya (Rinko Kikuchi), a rebellious, deaf Japanese teenage girl who refuses to speak, traumatized by the recent suicide of her mother and a sense that she is an outcast from society because of her handicap. She is bitter towards her father, Yasujiro Wataya (Kōji Yakusho), and boys her age, and is sexually frustrated. In response, she starts exhibiting sexually provocative behavior and attempts unsuccessfully to initiate a sexual encounter with her dentist. Chieko eventually encounters two police detectives who question her about her father. She finds one of the detectives, Kenji Mamiya (Satoshi Nikaido), attractive. She invites Mamiya back to the apartment she shares with her father. Wrongly supposing that the detectives are investigating her father's involvement in her mother's suicide, she explains to Mamiya that her father was asleep when her mother jumped off the balcony and that she witnessed this herself. It turns out the detectives are, in fact, investigating a hunting trip Yasujiro took in Morocco. Yasujiro is an avid hunter and during a trip in Morocco he gave his rifle, as a gift, to his hunting guide, Hassan, who at the beginning of the film sold the rifle to Abdullah.
Soon after learning this, Chieko reveals her real motive in inviting Mamiya to her home. She approaches him nude and attempts to seduce him. He resists her approaches but comforts her as she bursts into tears. Before he leaves, Chieko writes him a note, indicating that she does not want him to read it until he is gone. Leaving, the detective crosses paths with Yasujiro and explains the situation with the rifle. Yasujiro replies that he did indeed give it as a gift, there was no black market involvement. About to depart, Mamiya offers condolences for the wife's suicide. Yasujiro, though, is confused by the mention of a "balcony" and angrily replies that "My wife shot herself in the head. Chieko was the first to find the body. I've explained this to the police many times." The issue of the conflicting stories is never resolved. The detective stops at a bar to read Chieko's note. Within the film, the note's contents are never revealed. Part of it is momentarily visible to the viewer. The following is an approximate translation of the Japanese script beginning with the first line of the lower half of the notebook page:
(n.b., "[EDGE]" indicates the end of that particular line on the notebook page): ". . . I wanted [EDGE] . . . myself [EDGE] . . . that's why [EDGE] . . . connected [EDGE] . . . that is [EDGE] . . . although I cannot [EDGE] . . . I have to find out [EDGE] . . . message from my mother [EDGE] . . . I was not sure if I was loved by my mother [EDGE] . . . but that's not the case . . . [EDGE] thank you." [verification needed]
A fourth subplot takes place in the Americas where Richard and Susan's Mexican nanny, Amelia (Adriana Barraza) tends their twin children in their California home. Due to the shooting, she is forced to take care of the children longer than anticipated. Unable to secure any other help to care for them, she decides to take them to her son's wedding in a rural community near Tijuana, Mexico rather than miss it. Her nephew Santiago (Gael García Bernal) offered to take her and the kids to the wedding. They cross the border uneventfully and the children are soon confronted by the Mexican culture, and street scene. The revelry of the wedding extends well into the evening, but rather than staying the night in Mexico with the children, Amelia decides to drive back to the States with Santiago. He has been drinking heavily and the border guards become suspicious of his behavior. Despite having passports for all four travelers, Amelia has no letter of consent from the children's parents allowing her to take them out of the United States. Intoxicated, Santiago trespasses the border. He soon abandons Amelia and the children in the desert, returning to lead off the police (we never learn of his final fate). Stranded without food and water, Amelia and the children are forced to spend the night in the desert. Realizing that they all will die if she cannot get help, Amelia leaves the children behind to find someone, ordering them not to move. She eventually finds a U.S. Border Patrol officer. However, the officer is more interested in arresting her than helping to find the children— he doesn't believe her when she informs him that the children are Americans. Amelia sobs with love for the two children that she raised as her own. Somewhat reluctantly, the officer allows her to lead him back to where she thinks she left the children, but they cannot find them. Amelia is taken back to a Border Patrol station, where she is eventually informed that the children have been found and that their parents have agreed not to press charges. However, she will be deported from the US where she has been working illegally. Her protests that she had been in the US for 16 years and has looked after the children for the duration of their lives do not secure lenient treatment. At the end of the movie, the audience sees her meeting her son on the Mexican side of the Tijuana crossing, still in the red dress she wore for the wedding.
The fourth subplot, which happens after the other events, is actually shown along with the other narratives. There is no indication to show that it happens afterwards, other than a call from Richard Jones to his home which is shown from the American side at the beginning and the Moroccan side at the end. This gives the movie its strange disorientation which actually adds to the experience.
The film is actually about communication, or the lack of it, especially across international borders. Nobody can another as a human being. Americans see Moroccans, Mexicans see Americans. No one can understand one another.
 And the LORD said, Behold, the people is one, and they have all one language; and this they begin to do: and now nothing will be restrained from them, which they have imagined to do.
 Go to, let us go down, and there confound their language, that they may not understand one another's speech.
 So the LORD scattered them abroad from thence upon the face of all the earth: and they left off to build the city.
 Therefore is the name of it called Babel; because the LORD did there confound the language of all the earth: and from thence did the LORD scatter them abroad upon the face of all the earth.
Can we not build a temple together anymore? Is the vengeful God's punishment permanent?