The characters literally combine to mean “young person can be taught.” This simple phrase has evolved into a profound compliment about a person's potential and virtuous character.
The soul of this idiom comes from a famous story from the Han Dynasty, recorded in the *Records of the Grand Historian* (史记 - Shǐjì). The story features Zhang Liang (张良), a young man who would later become a brilliant strategist, and a mysterious old man, Huang Shigong (黄石公). While walking across a bridge, Zhang Liang saw the old man intentionally drop his shoe. The man arrogantly demanded Zhang Liang fetch it. Despite the rudeness, Zhang Liang patiently retrieved the shoe and knelt to help the old man put it back on. The old man simply laughed and walked away. He repeated this test twice more, each time with Zhang Liang showing immense patience and respect. Finally, the old man was satisfied and declared, “孺子可教也!” (“This child can be taught!”). He then gifted Zhang Liang a legendary book on military strategy, which helped him become a key figure in establishing the Han Dynasty. This story reveals the deep cultural meaning:
This idiom is still very much alive in modern Chinese.
The connotation is almost always positive and encouraging. The formality depends on the context, ranging from a formal assessment of character to a lighthearted family joke.