The traditional moral character of both Japanese society and Japanese individuals is built upon four key elements, which can best be compared to the Western concept of Virtues: On, Gimu, Giri and Ninjo. All four of these orbit and touch upon the Japanese concept of Honor, which combines elements of reputation, self-respect and personal moral/ethical code.I have looked up those concepts in other places both online and in books and really have not seen any explanation that is really any better than what is given there. I personally do not feel that my understanding of these concepts is sufficient to explain them in any detail. I do want to point out that the above mentioned concepts are not always congruent with one another and that there are other similar social mores in Japanese society beyond those four such as Kenson (a cultural form of humility less important than those mentioned) and the concept of face which, in many ways, is more important than any of the above mentioned ones (is considered by some a large part of the reason Japan attacked the USA and why the Japanese would not surrender easily).
Understanding these concepts can often help clarify the motivations and drives of anime characters, and can sometimes explain the differences between what we and the Japanese consider funny, tragic and/or dramatic.
The best translation for this term would be "Reciprocity". On is a virtue that requires the individual to acknowledge and repay debts he owes, including debts of honor. A source of I Owe You My Life situations.
Can be interpreted as "Piety". If one owes a debt (including a debt of honor) but cannot repay it, Gimu encourages the debtor to show allegiance to the debt-holder in lieu of true payment.
"Duty". Much more complicated than the Western concept of duty, Giri requires the individual to execute and balance his obligations as the highest function of an honorable life.
Usually translated as "Compassion". Ninjo requires empathy with others, and recognizes that all people are one, beneath the surface differences that karma imposes.
While these concepts can add to your understanding, or explain the characters actions in a different way then you currently view them, it is not really needed to know them to enjoy the manga. Generally I would place my interpretation as to how these concepts relate to the Ranma manga, and while I may do so at a later date, I do not feel like doing so at this moment (I do not agree with what is stated in the examples on the wiki at this time and do not feel like getting into an edit war about them). I will comment that the various engagements, Ranma's promises (beyond just the not actually said to Ryoga P-chan one), the seppuku pledge, the reason why Soun accepted the Gambling Kings possession of his dojo, and a few other things are tied into these concepts.
This post was last modified to the point of almost being entirely rewritten on 1/23/2010.