睡着 (shuì zháo) is a verb meaning 'to fall asleep' — it describes the moment of transitioning from wakefulness into sleep. The first character 睡 (shuì) means 'to sleep', and the second character 着 (zháo) here functions as a result complement, indicating successful completion of the action — literally 'to sleep successfully' or 'to get to sleep'. Unlike the standalone verb 睡 (shuì), which just means 'to sleep', 睡着 emphasizes the onset or achievement of sleep.

This word is commonly used in everyday spoken and written Chinese to describe falling asleep naturally, often unintentionally or after effort — for example, while reading, watching TV, or lying down tired. It's neutral in register and appropriate for both informal and formal contexts, though it’s more frequent in conversational speech than in formal reports or academic writing. Note that 着 must be pronounced zháo (not zhe or zhuó) when used as a result complement meaning 'to succeed in doing something'.