The characters literally combine to mean “[the awl's] sharp tip (颖) escapes (脱) and (而) comes out (出).” This paints a vivid picture of talent being so sharp that it cannot be contained.
The origin of “脱颖而出” is a famous story from the Warring States period (around 257 BC), known as 毛遂自荐 (Máo Suì zì jiàn - Mao Sui recommends himself). During a crisis, Lord Pingyuan of the Zhao state needed to assemble a delegation of 20 talented retainers to seek military aid from the state of Chu. He found 19, but struggled to find the last one. A man named Mao Sui, who had been in his service for years without recognition, boldly stepped forward and volunteered. The other retainers snickered, but Lord Pingyuan was intrigued. He compared a talented man to an awl in a bag, stating that if it were truly sharp, its tip would have emerged long ago. Mao Sui famously retorted, “If I had been put in the bag earlier, I wouldn't have just shown the tip, I would have pierced right through it!” On the mission, Mao Sui's eloquent and fearless arguments single-handedly convinced the King of Chu to form the alliance, saving the state of Zhao. His story cemented “脱颖而出” in the Chinese language as a symbol of hidden talent that, when given a chance, will spectacularly prove its worth. Comparison to Western Concepts: This is similar to the English idea of “a diamond in the rough” or “to rise to the occasion.” However, “脱颖而出” carries a stronger implication from its origin story: it often involves a proactive element. It’s not just about being passively discovered; it can be about seizing an opportunity to demonstrate one's ability, just as Mao Sui did. It celebrates both innate talent and the courage to show it.
“脱颖而出” is a highly positive and respected idiom. It's common in both formal and semi-formal contexts.
It is almost always used as a compliment and carries a connotation of earned success through superior ability.