The characters literally combine to mean “topple the nation, topple the city.” The structure emphasizes the scale of the beauty's influence—it's not just a city, but the entire country that is at risk.
The origin of 倾国倾城 comes from a story in the Book of Han (汉书). The court musician Li Yannian sang a song for Emperor Wu of Han to introduce his sister, Lady Li:
北方有佳人,绝世而独立。
In the North, there is a great beauty, peerless and standing alone.
一顾倾人城,再顾倾人国。
One glance from her topples a city, a second glance topples a nation.
The emperor, captivated by this description, asked to meet her, and she became his favorite concubine. This idiom is deeply tied to the historical trope of the 红颜祸水 (hóngyán huòshuǐ) — “a beautiful face is a disastrous water” — where beautiful women are often blamed for distracting emperors and causing dynasties to fall. Figures like Daji (妲己) or Yang Guifei (杨贵妃) are classic examples of women whose beauty was considered 倾国倾城 and was linked to the ruin of their respective dynasties. A Western cultural parallel would be “the face that launched a thousand ships,” referring to Helen of Troy. Both phrases describe a beauty so great it can cause war and destruction. The key difference is that 倾国倾城 is a standard, widely-used four-character idiom (a chengyu) in Chinese, whereas the phrase for Helen is a specific literary quote.
倾国倾城 is considered highly formal, literary, and poetic. It is not used in casual, everyday conversation.
The connotation is positive in describing the woman's beauty, but it retains its classical undertone of immense, potentially disruptive power.