This is Sanchin Kata as practiced at Gojuryu Karatedo Yoyogi Ryushinkan. Sanchin is the foundation for all other kata, and is generally considered to be the most important one to master. Only the Sanchin Dachi stance is used throughout. The lower half of the body is solidly rooted to the ground, while the punches draw their power from the earth through the legs and hips, enabling the strength of the whole body to be channeled and focused into one punch.
When properly executing Sanchin, all the muscles are flexed and tensed throughout the kata. Most styles of martial arts employ a version of Sanchin that follows the "hard" style of karate. In Gojuryu, however, the idea is to remain soft until a hard motion is executed, and then tense briefly at the right moment. This allows for better overall movement since continuous tensing is not conducive to easy or speedy movement.