Osu is one of the most familiar words in a Kyokushin dojo. It is used as a greeting, an acknowledgement and an expression of respect. Its meaning is closely connected with persevering under pressure.
Patience. Respect. Appreciation.
Training asks you to remain patient when progress feels difficult, respect the people training beside you and appreciate the time and effort that everyone brings to the dojo. Saying Osu is a reminder to carry those qualities into your practice.
You will hear it when entering and leaving the dojo, greeting an instructor, responding to a direction and acknowledging a training partner. The word connects the effort of physical training with the attitude behind it.
This explanation summarises the teaching quoted on the original Nintai website from the U.S. Kyokushin Karate Official Text Book Basics No. 1, by S. Oyama, Y. Oyama and M. Miura, published in 1981.