The tree is the only distinct piece of the setting, so we’re pretty sure it matters. (Also, if you check out the painting that inspired Beckett, you’ll see that a big tree features prominently.) Right off the bat you’ve got the biblical stuff; Jesus was crucified on a cross, but that cross is sometimes referred to as a "tree," as in, "Jesus was nailed to the tree." That Vladimir and Estragon contemplate hanging themselves from the tree is likely a reference to the crucifixion, but it also parodies the religious significance. If Jesus died for the sins of others, Vladimir and Estragon are dying for…nothing. (There’s that pesky "nothing" word again. You just can’t get rid of it in this play.)
But you can also think of the two men not as Jesus, but rather as the two thieves crucified along with Jesus. This fits quite nicely with gospel’s tale as Vladimir tells it; one thief is saved and the other damned, so Didi and Gogo are looking at a fifty-fifty chance. (Duality! Again.) 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. (Uncertainty! Again.) (Repetition! Again.)
There’s more. Vladimir reports that he was told to wait for Godot by the tree. This should be reassuring – it means the men are in the right place. Right? Wrong. As Estragon points out, they’re not sure if this is the right tree. And, come to think of it, they can’t even be sure if this is a tree or not. It kind of looks like a shrub.