The "Ako Incident" refers to two separate historical incidents taken together. First, a samurai lord attacked a high shogunal official in the shogun's palace during very important ceremonies. Drawing your sword in the shogun's palace was strictly forbidden and so, the lord was sentenced to commit ritual suicide the same day, his clan disbanded and all the clan properties confiscated. Then, about a year later, forty-seven of the former retainers of the lord avenged his death by attacking the mansion of the official and killing and beheading him.
On March 14, Genroku 14 (April 21, 1701 by the western calendar), Asano Takumi-no-kami, the lord of Ako, a small coastal domain in present day Hyogo prefecture near the border with Okayama prefecture attacked Kira Kozuke-no-suke, the shogunal master of ceremonies during ceremonies welcoming emissaries to the shogunate from the imperial court. Asano was arrested, interrogated and sentenced to commit ritual suicide that night and his domain confiscated. Because the punishment was administered so quickly, the actual reason for this initial attack are totally unknown. In his actual testimony, Asano said something like, "Although I should have said something about this earlier, I did not get a chance to and this is what happened." The popular explanation even from that time that Asano did not bribe Kira sufficiently and was bullied as a result is pure speculation. Other explanations include Asano having a fit of insanity or even that Kira or the shogunate engineered the incident to get Ako's superior salt making technology. (Even today, Ako is famous for its salt.) When a fight broke out in Edo castle, usually both parties were punished equally without regard to the reasons of either party, but in this case, Kira went totally unpunished. The shogunate position was that it was not a fight, it was a one-sided attack and praised Kira for not even reaching for his sword to defend himself, which would have made it a fight.
The events of the attack are much clearer. On the night of December 14, Genroku 15 (January 30, 1703 by the western calendar) a group of former retainers of the Ako domain under the leadership of former chief retainer Oishi Kuranosuke attacked Kira Kozuke-no-suke's mansion. They finally found him hiding in a charcoal shed, beheaded him presented his head at their lord's grave and then gave themselves up to the punishment of the shogunate. How to deal with this situation provided a difficult problem for the shogunate. On occasions when the law could not punish someone, it was possible for retainers or family members to take the law into their own hands in an official vendetta. But such a vendetta needed official permission from a lord or the shogunate. They had no such permission and probably couldn't get it since they were questioning the judgment of the shogunate. So for the shogunate, the question was whether to just treat the group as a criminal gang or to recognize their claims in some way. The incident itself was sensational since it seemed to show that samurai values of loyalty were still alive even after nearly a century of peace. Finally the shogunate decided that their claims should be recognized to some extent. Kira's relatives were punished and Asano's clan reinstated. But the band of former retainers had to be punished as well, in this case, by being allowed to commit ritual suicide rather than being executed by being beheaded as common criminals.
"Seppuku" means "cutting the belly." With the characters reversed it is read "hara kiri" which is a vulgar term because it evokes images of fish being slit along the belly to be cleaned. The tradition of ritual suicide began as an honorable way to die on the battlefield, rather than to be captured. This is a very painful way to die and sometimes the term is translated "ritual disembowelment." A blade is drawn across the belly to expose the entrails and then the person stabs himself in the throat. As actually practiced, usually the person only touched the dagger to his belly and then a person acting as second would behead him. In any case, this was considered an honorable death for a samurai and was distinguished from execution by simple beheading that would mark one as a criminal.
Please see Key Kabuki Words - Kabuki terms of "Unique Kabuki Stage Structures"