In Act III of the play, Emily has died. As she takes her place among others from Grover's Corners who have died, she requests to relive just one day of her life. Mrs. Soames tries to discourage her, but she insists, promising to choose a happy day. Mrs. Gibbs replies:
No. At least choose an unimportant day. Choose the least important day in your life. It will be important enough.
Emily chooses her twelfth birthday and watches herself in life when she had been a child at home with her family. As she watches the scene before her, as her family goes about its daily life, Emily becomes more and more upset and begs to be taken back up the hill to her grave: "Oh! Oh. It goes so fast. We don't have time to look at one another." She breaks into sobs.
The quotation in your question is found in Emily's goodbye to the world as she prepares to leave:
But first--wait! One more look. Good-by, good-by, world. Good-by, Grover's Corners . . . Mamma and Papa. Good-by to clocks ticking . . . and Mama's sunflowers. And food and coffee. And new-ironed dresses and hot baths . . . and sleeping and waking up. Oh, earth, you're too wonderful for anybody to realize you . . . Do any human beings ever realize life while they live it--every, every minute?
After her death, Emily realizes that it is not the extraordinary but the very ordinary aspects of life that are in fact precious. It is these everyday wonders that escape our recognition, understanding, and appreciation because we take them all for granted as we hurry through our days. In answering Emily's question, the Stage Manager tells her that "saints and poets" perhaps realize life, at least to some extent. This scene in the play--truthful and thought provoking--is very moving indeed.