Hope this helps.
"The famous "OSS" has many origins. The first definition of "OSS" is an abbreviation for Onegai Shimasu, which translates into a request, a solicitation, an invitation like "please", "if you may" or "With your permission", much used when inviting a partner to train.
The second definition of "OSS", also known as "ossu" means Oshi Shinobu, which conveys the idea (the literal translation has nothing to do with the context) of "persevering when pushed" in other words, never give up, have determination, grit and withstand the most arduous of training. Carrying on without giving up, under all kinds of pressure- that's the idea of inner strength so common in Asian culture.
According to Miyamoto Musashi, in the book "五輪書, Go Rin No Sho", the samurai would use three types of shouts: One before combat, the second during combat, when attacking to muster great strength and the third after the fight, to celebrate victory.
"Oss", beyond demonstrating strong spirit and determination before a fight, is also used to suggest or confirm a piece of information. Thus whenever a Sensei asks or informs something, the response is "OSS!" it is the response that will confirm understanding."