The tree is the only distinct piece of stage props., so as a symbol it is immediately identified. I think it might be worth while to investigate the biblical implications. Jesus was crucified on a cross, but that cross is sometimes referred to as a "tree," as in, "Jesus was nailed to the tree." Vladimir and Estragon contemplate hanging themselves from the tree and this is a reference to the crucifixion, but it also parodies the religious significance. If Jesus died to free the (Christian) world from sin, Vladimir and Estragon are dying for…nothing.
Vladimir and Estragon might also represent the thieves crucified alongside Jesus. This fits quite nicely with Vladimir telling the gospel story; one thief is saved and the other damned, so Didi and Gogo are looking at a fifty-fifty chance. The uncertainty that stems from inconsistency between the four gospels is fitting, too, since Vladimir can’t be certain if Godot is coming to save either one of them. Estragon points out that the duo is not even sure if this is the right tree.
The tree’s random sprouting of leaves in between Act I and Act II symbolises regeneration! Take a look at Vladimir’s line early in Act I, when he says, "Hope deferred maketh the something sick, who said that?" Vladimir is referring to the biblical: "Hope deferred makes the heart sick; but a desire fulfilled is a tree of life."
So the tree blooming would suggest that it might represent the tree of life. f course, as far as we can tell, no desires have been fulfilled. This could mean that the proverb is completely without truth and reason, which fits with Godot’s general stance on religion. Then again, the tree’s sprouting leaves could be an ironic symbol pointing out that, far from fulfilled desires, hopes have been deferred yet another day – much like Vladimir’s ironic claim in Act II that "things have changed here since yesterday" when, clearly, nothing at all has.