These characters combine to paint a vivid picture. 粗心 (cūxīn) means having a “rough mind”—one that isn't fine-tuned to catch details. 大意 (dàyì) literally means “big attention,” which implies that one's focus is too broad and spread out, not concentrated on the small, important things. Together, 粗心大意 (cūxīn dàyì) describes someone whose mind is too “rough” and whose attention is too “big” to handle tasks with the necessary precision.
In Chinese culture, particularly in education and the workplace, there is a tremendous emphasis on being 认真 (rènzhēn) - conscientious and meticulous. Doing a task with care and precision is a highly respected quality. 粗心大意 is the direct and unwelcome opposite of this ideal.
Parents and teachers constantly use this phrase to scold children for making preventable errors on homework or exams. A student who knows the material but loses points for simple calculation errors will invariably be told they are too 粗心大意.
This idiom is extremely common in everyday life.