"The unexamined life" refers to a life lived by rote under the rules of others without the subject ever examining whether or not he truly wants to live with those routines or rules. According to Socrates, this type of life was not worth living. Rather than living an unexamined life, Socrates chose death, and these words are attributed to the philosopher during one of his last speeches before his suicide.
The quote "An unexamined life is not worth living" was published in Plato's "Apology." Sometimes called "The Apology of Socrates," this book contained Plato's recollections of Socrates' last speeches.
Socrates was given two choices: leave Athens or live the rest of his life in silence. The philosopher was not willing to leave his home, and he was not willing to be silent. Being silent implied his agreement with the government, and in his eyes, this equated to living an unexamined life. Unwilling to live that type of life, Socrates killed himself.
In modern times, the phrase has come under scrutiny for being elitist. Critics of the idea claim that only the elite can live an examined life. The huddled masses, in contrast, have to work within the system just to stay alive. They do not have the choice to opt out of something that they do not believe in, whether they examine it or not.