If I understand you correctly, it appears that you wish for an analysis of the symbolism of the play as a whole and not an exploration of individual symbols as they appear in the play.
A symbol, by definition, refers to an object or situation which is used to represent an idea or belief in a non-literal sense. The author utilises literal scenarios or objects to evoke a deeper understanding of, or insight into an idea which he/she may believe has universal application and relevance. Obviously, there would be different interpretations in this regard since it is natural for us to perceive the author's supposed message within different contexts.
And so it is with Samuel Beckett's, Waiting for Godot. The author had consistently claimed that he had not written the play with any particular purpose in mind and was frustrated by the fact that so many interpretations unnecessarily complicated something so simple. Beckett repeatedly rejected any appeals for clarification on either characterisation, plot or purpose of his remarkable play. That therefore leaves us with the task of finding meaning in the work.
The play is a symbol for the purposeless nature of man's existence. Vladimir, Estragon, Pozzo, Lucky and the boy, all represent mankind whilst Godot, it appears, represents the ethereal, the unknown. There is no meaning or purpose in what the characters say or do - it is all a futile exercise. The implication is that trying to find any meaning becomes an exercise in absurdity, best illustrated by Lucky's garrulous, garbled diatribe in the first act.
The situation in which the characters find themselves alludes to mankind's self-indulgent nature. In order for us to support our belief in our self-importance, we need to be seen to be investing our time in finding answers and being productive, in some way or another. The play brilliantly depicts the folly of this notion, since none of the characters actually resolve any of their issues and they become victims of the march of time: they become older whilst waiting, Pozzo goes blind, Lucky becomes mute. In the end, they are stuck at exactly the point at which they were at the beginning of the play.
The characters are caught in an ever-repeating cycle, forgetting the past either willingly or unwittingly, and therefore not learning from it. Their existence has a profoundly, almost ritualistic, repetitive nature about it. This further emphasises the purposelessness of life - time passes on, but we find ourselves, as far as our spiritual or intellectual evolution is concerned, right back where we started. Our supposed scientific, religious and philosophical insights and developments have lead us somewhere, but nowhere. There exists just as much meaning as there is in Lucky's insight.
Symbolism is the key factor in Waiting for Godot; however, in order to understand the symbols in the play, you have to understand where Absurdist Theater came from and what it entails.
Samuel Beckett wrote Waiting for Godot sometime between 1948 and 1949; however, it was not first performed until 1953. At the end of World War II, a change in theater occurred. While Surrealism had existed in the 1920s, it resurfaced after the war not as a fantastical element but as a moment of intense emotion and awareness that freed people from the ordinary. Post World War II found France with a crisis of "moral order." France had been controlled by Nazi Germany for a time, and then was freed. The result left some confusion over what was considered moral and what wasn't. Under this new confusion, Existentialism came into being. "Theater of the Absurd," is the best classification of Waiting for Godot, which is a part of Existentialism. Absurdist Theater is a term given to plays that show "a hostile meaningless universe looming large over individuals who are unsure of or unconcerned about what to make of themselves, their situation, and other things they encounter." When you think about France during and at the end of World War II, it is easy to understand how it embraced Absurdist Theater.
The world of Waiting for Godot is not our world. It resembles our world, but it is not intended to take place in the world that we experience. Didi and Gogo are supplicants of Godot. While they have no power in this world, they feel that Godot must have some type of power and possesses the things they do not have: home, family, friends, servants, books, money, and a horse. There is a bit of fear from Didi and Gogo that they might be slaves of Godot, but they really do not know. Their relationship to Godot is not as clearly defined as it is with Pozzo and Lucky.
Certain aspects of our world exist in the world of Waiting for Godot, such as dancing and singing to pass the time, and the Bible. There is a Fair, which is never seen, but it is both happy and troubling. There is whimsical imagery when talking about the fair, but the eventuality of Lucky's sale offers some foreboding. Time and geography are different in the world. Didi do not know if they have been sitting in the same place or if it has changed.
As in all Surrealism and Existentialism, symbolism plays a key part in the production of the play. I will discuss four major aspects of symbolism: Duality, the tree, the character's hats, and the “waiting”/ time; however, there are more symbols throughout the play such as Gogo's inability to get close to people due to his sense of "smell" (his repulsion of the banality of humanity), Lucky and Pozzo and the connection to self-slavery and how the slaver and the slave are intertwined (Pozzo doesn't know how to do anything. He would be powerless without Lucky's help), the oncoming night representing death, and Lucky's dance "The Net"- showing how he has been enslaved so long he can no longer dance true dances of joy, but can only stretch for freedom before falling back into slavery.
Duality. 50/50 chances are a running theme in the play- in the conversation on suicide it is decided that the tree branch may or may not break, concluding that one person may live and one person may die. The two thieves one may be saved while the other id damned in the end. Godot himself may only save one of the two main characters. The entire play is bound in pairs: Vladimir and Estragon are bound together for what seems throughout time. There are two thieves. Pozzo and Lucky come and leave as a pair. Cain and Abel the first two brothers are discussed. The tree's movement between life and death throughout Act one and Act 2. In addition, it must be noted that the play only has two acts rather than the standard three of the time.
The theme of duality that runs through the play is intended to express the ambiguity of not really knowing about God, time, existence. It shows the idea that we all have fifty-fifty chances in who we are and where we will eventually end. Either we are right or we are wrong in our decisions about what we are supposed to do with our life.
The Tree. The tree is the only prominent piece of the set. It is discussed that the tree may be a willow that has given up weeping and is now dead. Didi and Gogo are to wait beside the tree in order to meet Godot. However, they are concerned that it is the wrong tree despite the fact that it is the only tree in what the audience can perceive as the world. In general the tree is to have two branches that give the tree the impression that it is a cross, contributing to the image of a cross. This connects to the idea that the tree itself represents regeneration or resurrection. A side joke that is hidden in the text of the play is that both Didi and Gogo consider hanging themselves from the limb of the tree but decide against it because the limb will not support them. Under the ideals of Catholicism, the salvation promised through the cross does not support those who commit suicide.
The Character's Hats: Each character has a hat (except the boy). In the original play, all characters had bowler hats, but in several modern versions, directors have chosen to have various styles, so the audience can track the hats' movements. The bowler hats are a nod to Beckett's joy of Vaudeville Theater where the majority of the performers wore bowler hats. Likewise, the bowler hats are generally used through blocking with vaudevillian hat tricks. The hats represent the identity and personality of each of the characters. Vladimir (Didi) focuses almost completely on his hat. Throughout the play, he is the thinker. Estragon (Gogo) is fixated on his boots and his hat is secondary. He is the realist of the two companions. He has his feet on the ground. Lucky can only think with his hat on, and Pozzo shows his dominance over Lucky by removing the hat and returning it at his will. Lucky's hat is also used when Didi decides to wear it. This indicates Didi's desire to change himself. It is interesting that Didi chooses the slave rather than the master when he makes this shift. Finally, the hats are used to show that uniformity comes from removing your personality. Every time the group agrees or comes to a conclusion, all hats are removed.
Finally, the symbolism of Gogo and Didi “waiting.” At one point Gogo calls it “hope deferred.” Both of the main characters are preoccupied with passing the time. It is symbolic of how some people are so preoccupied with waiting for good things, bad things, resurrection, death, the lives and choices of others, their own failings, etc. they never move forward in life. The continual ramblings of Didi and Gogo trying to entertain themselves during the “waiting,” exemplifies how people distract themselves from their own hopes and dreams. Neither Didi nor Gogo come to any realizations about their lives throughout the course of the play and this is shown in the final line "Yes, let's go." The statement gives the expectation of movement, yet in the staging of waiting for Godot, neither Didi nor Gogo move. The play is clear that there should be an overall sense of lingering by the two actors giving the audience a clear statement that they will not actually leave from where they are seated. This hints back at Pozzo’s statement when he plans to leave that he cannot go forward. “Such is life” is the reply. Pozzo must get a running start in order to leave the stage. It is important to note that Pozzo loses his watch before he is able to move forward along the road. (He loses his awareness and connection to waiting.) Gogo and Didi remain, however, eternally focusing on the waiting.
Beckett's play is not exactly a symbolist play. That is not to say that it does not have symbols. There are symbols galore in the play but the point is that it does not want to fix any symbolic interpretation on itself. It rather vaguely opens up multiple symbolic layers to seduce the reader into one or the other. None of these, on its own is a substantial one, however.
The greatest seductive symbol in the play is the figure of Godot which is seen to represent God, existence, meaning, the gaze of the other, a social big-brother figure, an absent centre of authority and so on.
Waiting as a condition of being is yet another symbolic act in the play.
There is a symbolic import in the repetitive circularity of action in the two acts.
The boots, the hats, especially Lucky's thinking hat which produces his great speech are all symbolic objects.
The tree, the country road, the leaves that appear on the second day, the way the two tramps and Lucky and Pozzo fall in the shape of crucifixion in the second act, the social category of the tramp--all these are symbolic in the play-text.