For a long period in the history of humans has time been used to sequence, or to measure the duration of events and intervals between them. Without time we are crippled; there would be no past, no present or no future - we would just be drifting around aimlessly with nothing to expect. Time adds a sense of order and helps us understand our existence a lot better as it helps us gain knowledge of the world around us. Beckett and Ionesco both understand time in the same way, and this is shown through their plays 'Waiting for Godot' and 'The Bald Soprano'.
The very title of 'Waiting for Godot' shows that the play has a lot to do with time, where it is shown as being cyclical (the events occur in a cycle). The play's central characters Vladimir and Estragon are forced to whittle away their days in the hope that another character named Godot will arrive and add a little sense of direction to their lives. Godot never comes, and so Vladimir and Estragon simply have to endure until their acquaintance shows up.
Beckett introduces this idea that the protagonists are waiting for Godot early in the play, which also allows the audience to expect his arrival, which would then add to the overall plot of the play. 'Waiting' is also the reason for the play to take place - Vladimir and Estragon could easily leave their situation and go separate ways (or even kill themselves), but they refrain from doing this [shown below].
ESTRAGON: Let's go.
VLADIMIR: We can't.
ESTRAGON: Why not?
VLADIMIR: We're waiting for Godot.
In the play, Vladimir and Estragon aren't even sure if they are waiting in the right place, or whether they have even met Godot at all. While they wait, the pair try to pass the time by indulging in mundane activities (taking off a boot and putting it back on, the switching of the hats), asking each other questions, and even going as far as to insult each other. They meet two other men, Pozzo and Lucky, who join them and then continue what Vladimir and Estragon were doing before - nothing. After Pozzo and Lucky leave, nothing changes. Vladimir and Estragon keep at their task, when Vladimir suggests that it wasn't the first time they met with Pozzo and Lucky (even though they acted like complete strangers). Estragon doesn't seem to recall a thing, but then again he doesn't remember much throughout the play (his memory is faulty). When the actions done on one day don't necessarily have any bearing or firmness on the next, time seems to lose its meaning.
Later on, a boy shows up and tells the two that Godot won't be coming on that day, and that he would definitely be coming on the next day. Once again, Vladimir suggests that this has happened before, but doesn't seem to recall it perfectly.
Vladimir and Estragon's situation suggests that they have been at this together for so long, that they don't seem to have any sense of time. There is no mention of a timekeeping device, hence they cannot tell the time. Nightfall...