What is the relevance of this quote from Waiting for Godot: "Down in the hole, lingeringly, the grave digger puts on the forceps."
The play, Waiting for Godot, is at its heart, a play about what defines life and death. What does it mean to be alive? Existentially alive? Vladimir's quote is in reference to something that Pozzo said as he was leaving the stage just a page or two before this. Pozza expresses his extreme frustration with Vladimir's questions about time and when things happened. Pozzo proclaims
Have you not done tormenting me with your accursed time! It's abominable! When! When! One day, is that not enough for you, one day he went dumd, one day I went blind, one day we'll go deaf, one day we were born, one day we shall die, the same day, the same second, is that not enough for you? They give birth astride of a grave, the light gleams an instant, then it's night once more.
What Pozzo means is that life happens in an instant and is gone before we know it. The minute we are born we are dying. Time is irrelevant because it all ends in death, so getting caught up in the details of life and "when things happened" is a waste of time because time is meaningless.
Once Pozzo is off the stage, Vladimir has some time to contemplate Pozzo's declaration. He is a bit disgusted by Pozzo's pessimism, and alters the quote a bit. His additions to the quote suggest that the time between and death at least a bit longer than the instant that Pozzo says, but his language also points out the struggles of life. Vladimir says
Astride of a grave and a difficult birth. Down in the hole, lingeringly, the grave-digger puts on the forceps. We have time to grow old. The air is full of our cries.
While the quote still uses the image of life and death being at almost the same time, the fact that the birth is difficult and takes more time, and that the grave-digger must use forceps to bring out the life means that there is more time than the brief gleam referenced by Pozzo. The grave-digger acts lingeringly -- taking his time. Vladimir mentions that the air is full of our crying -- that there is time for crying, not an instant death. He directly states that "we have time to grow old." Vladimir believes that there is more to life than just the process of dying: we will struggle to make something of our lives before we die and it will be a difficult life, but it will be a life, not only a death.