Vladimir asks Estragon what they should do while waiting for Godot, who never arrives, leaving them in a state of stasis. Estragon responds by saying, "What about hanging ourselves." Vladimir says, "Hhhm, it'd give us an erection." That idea makes Estragon "highly excited." The two, however, quarrel over who should hang himself first on the bough of a nearby tree. They decide, in the words of Estragon, that it is "safer" not to do anything, but to continue to wait.
The dialogue between the two friends is darkly humorous. Something as momentous as a suicide is reduced to the desire to have an erection and a quarrel over who should go first based on who weighs more. This shows the absurd quality of life, in which taking off a boot and killing oneself are reduced to the same level of banality.
It is significant that the two old men decide to continue waiting rather than acting even though they say that they are bored with life and bored with waiting. Godot, a seemingly godlike figure to whom they have made some sort of request, never seems to arrive.
The play was written in 1949, shortly after the end of World War II, and reflects a time when, to Beckett, many Europeans were like Estragon and Vladimir: not able to remember the past (and thus learn its lessons) but also metaphorically paralyzed and unable to move forward, even to suicide.