The inscription is taken from Confucius's Analects expounding on the didactics in nurturing Man's outlook on life.
The cat and butterflies represent a wish for longevity, the word "cat" (mao) having the same sound as the Chinese word for "septuagenarian," while the word "butterfly" (die) is homophonous with "septuagenarian" or "octogenarian." The wish for longevity is reinforced by the rock and chrysanthemum, symbols of long life.
This subject of numerous geese and reedy banks was popular in paintings from the Song dynasty onwards, and may represent autumn, particularly in combination with chrysanthemums (representing the ninth month).
See Moss, Graham and Tsang, A Treasury of Chinese Snuff Bottles, no. 1026 for an olive-green overlay white glass snuff bottle attributed to Li Junting, also carved with a cat and butterflies.