Ah the question that tends to drive all theater students quite mad, especially when they have professors that expect them to give a clear concise answer to the question.
To be honest it is a Samuel Beckett play don't expect anything to be obvious or clear cut. I spent a decent amount of time trying to figure out the answer to this question myself when I was in school, but never arrived at any definitive conclusion, but I have heard some rather entertaining theories. One very common theory is that the characters are waiting for God. One person in my class went so far as to do a great amount of background research on Beckett at the time he wrote this play. She discovered that he was in Germany at the time and started looking for German words that match or were close to 'Godot' in order to figure out what the title meant. She concluded that it translated into "dead dog" so by her definition they were waiting for a dead dog that won't come.
As I said I have heard some entertaining takes on this one.
So I wish you the best of luck and a good time trying to reason this one out for yourself.