The meaning of "OSU"
"Osu" is made up of two kanji, "o" meaning to "push" which symbolizes one hundred percent effort and "su" means to "endure". Combined, "osu" is a pledge to do one's best and endure. The martial arts require a great deal of discipline, which involves a great deal of self-reflection, and self-reflection is more concerned with irrefutable truths than with rewards.
Some students will pretend to train hard only when they believe their sensei is watching. These types of students devote more energy towards attracting their sensei's attention than to learning martial arts. In other words, their efforts are not "silent". Students are in class to learn martial arts, not to impress their sensei. How much they learn depends solely on how hard they work. If they put forth their best efforts only when the sensei is watching and are lazy the rest of the time, this will inevitably be reflected in their techniques.
It is said that a flower blossoming deep in a secluded forest is no less beautiful than one growing in a garden where everyone can see. Students who study martial arts will sometimes say "osu" in a normal speaking voice, but just as often, they will loudly shout this word, which can substitute for "hello", "good-bye", "yes", "ok", or "I understand". No matter how or when it is said, however, "osu" reaffirms one of the most important lessons in martial arts.
Source: "The Empty Hand"