Though it might not have been the intent of the question, this precise issue marks the purpose of not only the play but of all existence. The character of Godot marks the driving force of the Vladimir and Estragon because it is for whom they are waiting. Essentially, the purpose of both characters, the reason why they are there, is to eagerly await the arrival or mere presence of Godot. Beckett denies that Godot is "God." Of the many contradictions and complexities that Beckett represented, it would be too simple to presume that the character of Godot would be the higher force. However, one can make the argument that Godot represents anything for which we are waiting. Any external force that we believe will answer our queries, stop the pain of modern insecurity, and provide the Sartrean "bad faith" answer of totality can be seen as "Godot." Both characters believe that Godot will provide the answers, and that this faith in absolutism can be what the character is meant to represent. It can be a religious force, a material object, a state of being in the world, or anything that is perceived to alleviate the difficulty of living in the modern setting.
In the play Waiting for Godot, the central characters, Estragon and Vladimir, wait for a character named Godot, who never arrives. Godot is therefore a projection of the characters' unrealized and at times vague hopes and dreams. While the characters often refer to waiting for Godot, they cannot recall where they are supposed to meet him (other than knowing in a vague sense that it's by a tree). At times they consider ending their lives but then decide to continue to wait for Godot, though they cannot really determine the benefits or rewards of doing so. Godot represents their vague sense that their lives will eventually have promise or some type of meaning or conclusion, though it's unclear when this promise or conclusion will arrive, if ever. Godot constantly promises to arrive but never actually does so. The vagueness of Godot is one of the absurdist elements of the play and represents the idea that the meaning of life is unclear and perhaps nonexistent.
Instead of the symbolist way of approaching 'Godot' as a word-play on 'God' and thus reducing the play to a haplessly restricted philosophico-religious reading, I think, Beckett's body of work allows us to see Godot as a pure-signifier, for which there is no signified. It is a Derridean post-structuralist notion of the absent centre that informs Godot, who is absence incarnate. Beckett alludes to an excluded centre in the form of Godot, the absent dictator in the world of the play. Godot is like a pure-symbol which subsumes all the simplistic symbolic ideas that it can be said to represent. It is death, God, meaning/essence of life, the power-centre--all at the same time. And as Beckett would say, it has something to do with Estragon's boots. Godot marks an immanent power in spiritual terms and a 'beyond' in terms of theatricality, as Eric Levy says, a radical focalization of the offstage. Finally, Godot acknowledges the slippage between the word and the world in a way highly reminiscient of Joyce and even anticipates the postmodernist critique of realistic representation.
Depending upon how you wish to approach/decipher any meaning to the play it really is down to you the reader as to how you interpret the mysterious (off-stage) character that is Godot.