Lord Katsumoto wanted to "open" the Emperor's eyes to show him how him listening to the counsel of Omura and his cronies is killing off the old ways of the Japanese culture (and of the ways of the Samurai: honor, loyalty, sacrifice) by embracing the ways of the "west". The Emperor was blinded by all his other counselors trying to get him to "improve" the Japanese Empire with all the new and wondrous technologies (weaponry/arms/military might) to improve their status with the other nations in the world. When Katsumoto's counsel was originally ignored, he felt he failed and left to go live in his old village where life was more simple and more in line with the ways of a Samurai. Nathan Algren was crucial intel for him to decide how to understand his "enemy" (and of the western culture) and how to proceed to getting the Emperor to listen to him. When Nathan Algren changed his life it only reaffirmed his convictions that the way of the Samurai is relevant and important.
Soooo, as Katsumoto was the Emperor's former mentor and he gave him the ultimate lesson by giving up his life and of the Emperor's loyal subjects (his Samurai) to make him understand the old ways is much more important than modern progressive ideas of the west.