Combining them, 安史之乱 (ān shǐ zhī luàn) literally means “The Rebellion of An [Lushan] and Shi [Siming].”
The An Lushan Rebellion is arguably the single most important turning point in the latter half of Chinese imperial history. It serves as a stark dividing line between the “High Tang” (the prosperous, confident, cosmopolitan early period) and the “Late Tang” (a period of decline, fragmentation, and xenophobia). Its cultural footprint is immense. The suffering and chaos of the war were immortalized by some of China's greatest poets, most notably Du Fu (杜甫). His poems, which vividly describe the destruction of the capital, the suffering of the common people, and his personal grief, transformed Chinese poetry, shifting its focus from courtly elegance to gritty realism and social commentary. A useful comparison in Western culture would be the Fall of the Roman Empire. Just as the fall of Rome marked the end of the classical era and the beginning of the “Dark Ages” in the European consciousness, the An Lushan Rebellion represents the shattering of a perfect, prosperous world for the Chinese. It's a cultural touchstone for the profound tragedy of a golden age lost, a lesson in how quickly prosperity can turn to dust due to political corruption and unchecked ambition. It embodies the historical value of remembering catastrophic failures to prevent future ones.
As a historical term, 安史之乱 is used almost exclusively in formal or educational contexts. You won't hear it in casual daily conversation unless the topic is history.
The connotation is always extremely negative, serious, and large-scale. It implies not just a problem, but a foundational collapse.