How does the play Waiting for Godot show that time is meaningless?
The mere fact that the characters and therefore the audience aren't sure about how much time passes from scene to scene or act to act contributes to the theme of the meaninglessness of the passages of time. The most obvious example of the questioning of time is the fact that the tree in Act 1 doesn't have leaves, but there are leaves visible at the start of Act 2. Even at the height of growing season, leaves don't literally appear overnight, so that leaves us wondering how much time as passed, and why are the two men so unaware of it? It is actually kind of frustrating that they don't even comment on the leaves -- we only learn of it through observation or the stage directions. Obviously nothing of note happened in the days or weeks that have passed, thus time is meaningless if there is nothing of importance to fill the time -- no obligations, no job, no change.
Another example of the meaningless of time comes in Act 2 when Pozzo and Lucky return. Their circumstances have completely changed (seemingly overnight) in that Pozzo is now blind and Lucky is now actively leading Pozzo, rather than being commanded along like we see in Act 1. It isn't likely that their circumstances changed so dramatically overnight and they have come to such an easy/nonchalant reversal of roles overnight, but that is how is appears. The passage of time though is meaningless in that it doesn't change the end result. Even though something HAPPENED to these two characters, it ultimately doesn't matter as they adapted to the new situation and trudged on through their lives.
Vladimir and Estragon clearly don't care that are seemingly wasting time waiting for Godot to give them guidance. They see little other option to make MORE of their time on earth and don't pursue even any other thoughts about what else to do with their lives. They are existentially dead. This point of the play shows the ultimate meaninglessness of time.