I answered a similar question about this play awhile ago here on eNotes which is applicable to your question:
Man is always searching for God, but he never comes. Or, man is always waiting for someone to make his life better, but this never happens, that "person" never comes.
At the end of the play, Vladimir and Estragon decide to leave, to stop waiting for Godot, but do they go? No. They stay. Nothing happens. It's absurd - theatre of the absurd. Life is absurd. God is existential. If he's there, he doesn't care. And men waste a lot of time in life trying to figure out if he is coming. But he never does. It's up to us to figure out our reason for existence, and if there is a God, he watches with disinterest
So, think about all that is wrong with life in the modern world - lonleliness, isolation, despair, endless pursuit of getting ahead, furtively trying to find happiness and not being able to do so, and you will have the gist of what the characters are waiting for. They are waiting for all of these things, and in the philosophy of "theater of the absurd" the wait is in vain because "Godot" never comes.
If you read the helpful information here on eNotes, you will see that the play was written after WWII and it was written in French by an Irishman. Remember what happened to Europe in the war? It was in ruins. Remember that France was one of the countries invaded and occupied by the Nazis. The Nazis destroyed many beautiful architectural wonders, artworks, etc., and the French were left defeated and disheartened. Out of this malaise came the "theater of the absurd" with its gloomy, existential portrayal of life.
I would just like to add something to the answer posted. This centralization of waiting in itself and for itself is also a subversion of the conventional narrative use of waiting situations simply as an intermediate stage or even a sort of a filler.
Waiting for Didi and Gogo imply a coupling of the necessary and the impossible and the crucial point to note here is that they wait in spite of knowing fully well that Godot will never come and it is a waiting (for whatever it may be order, God, Meaning of life or anything else) ad infinitum. The hope is not there in the possibility of the arrival but perhaps there is courage if not hope in the persistent act of waiting.