These characters combine almost literally to form the idiom's meaning: “one part knowledge, half part understanding.” The imagery is vivid—it paints a picture of someone possessing only a fraction of the necessary knowledge and comprehending even less. This combination emphasizes the fragmentary and incomplete nature of the understanding.
The idiom 一知半解 is deeply rooted in the traditional Chinese cultural emphasis on deep, rigorous scholarship (学问 - xuéwèn). Confucian values prize humility, thoroughness, and true mastery. To be accused of having a “一知半解” understanding is a serious criticism, suggesting a lack of intellectual diligence and responsibility. A Westerner might be tempted to equate this with “a jack of all trades, master of none.” However, there's a key difference. “Jack of all trades” can sometimes be neutral or even a compliment, suggesting versatility. 一知半解 is never a compliment. It's a pointed critique of someone's grasp of a *specific* topic, not their overall range of skills. It suggests that their current level of knowledge on that topic is not just incomplete, but useless or even dangerous. It reflects the cultural belief that superficial knowledge is worse than admitting ignorance, because it can lead to arrogance and grave errors.
This is a common idiom used across various contexts, from casual conversation to formal academic writing.