"The unexamined life is not worth living" is a famous dictum supposedly uttered by Socrates at his trial for impiety and corrupting youth, for which he was subsequently sentenced to death.
The dictum is recorded in Plato's Apology (38a5–6) as ὁ δὲ ἀνεξέταστος βίος οὐ βιωτὸς ἀνθρώπῳ (ho dè anexétastos bíos ou biōtòs anthrṓpōi, literally "but the unexamined life is not lived by man").
For Socrates, to be separated from elenchus by exile (preventing him from investigating the statement) was therefore a fate worse than death.
[1] Socrates believed that a life devoid of introspection, self-reflection, and critical thinking is essentially meaningless and lacks value.
This quote emphasizes the importance of self-awareness and questioning one's beliefs, actions, and purpose in life.