Raven did a good job explaining the pronunciation of "osu" but I think the more important point is its usage. It is used by many NON JAPANESE in martial arts to convey a variety of meanings: "Hey, congratulations, good job," etc. It's kind of an all purpose slang to Westerners, thinking it makes them more Japanese. Truth is, it is an impolite slang with very limited correct application, and really has no place in the dojo.
My sensei spent many years training in Okinawa and said he never heard it used. His Okinawan master told him it's rude to use it. This is the danger of cultural appropriation when one does not understand the culture or appreciate the linguistic nuances. "Osu!" sounds cool and may be fun to say, but would raise eyebrows if said to a Japanese martial artist is most all cases. Better to drop this word from your Japanese vocabulary and find a more polite and proper way to express your thought.
PS - I think there are 46 hiragana and 46 katagana (not counting the little accent marks next to some of them which modify the sound.) Sounds complicated, but really very simple - each character is a phonetic syllable (na, ni, nu, ne, no, etc) with no ambiguity in pronunciation. Kanji? You're talking YEARS of study to integrate it into your reading skill set and constant exposure to it to remember it all.
Yes, I've read the studies, and seen the plethora of comments online about it. Three things come to mind, in response:
1 ) As I mentioned, this is specifically about the linguistics of it. There are plenty of other posts about its meaning and usage.
2 ) On the topic of its meaning and usage, it is not a rude term by default-- it's possibly multiple polite terms rudely shortened (ohayoo gozaimasu, onegaishimasu). Regardless, I wouldn't say it to a Japanese person unless they were younger and/or lower rank than me, and it were in a context in which that person understood it to be encouragement.
3 ) While it comes 100% from Japanese lexicon, like many loan (and shared) words throughout the world, its meaning is clearly regional. I learned it originally from Kyokushin Karate (studied in Canada), which was the second art I studied seriously (after TC Kenpo). That school was where I learned many of the Japanese-Martial-Art traditions, and both genuine and bastardised ettiquette and terms.
"Osu!" was strongly encouraged there, and meant a plethora of positive things: affirmative, respect, I understand, I will comply, etc. It has become its own tradition in North America, and is no less valid just because it isn't used that way in Japan, than any of the other terms we use in our culture.
You know what a fag is, right? (I imagine that word's gonna get filtered out by the bot.) If it does, it furthers my point, because the three-letter word I wrote means a stick or cigarette in England. In fact, its origin is to mean a stick you specifically intend to burn on a fire (which, incidentally, is probably the origin of why it's so offensive-- as that IS a horrible thing to call a person).
Of course, in North America, it's a homophobic slur. Same word, even from the same language.
So who dares claim the right to decide that Osu! can't be used as a term of respect and tradition in North America? Seems a pretty arrogant and pointless claim, to me.
That said, it's still a good idea to be aware that it can be rude when used in Japan! So I'm not knocking spreading that awareness; I just believe in dualistic natures.
Osu!