In this film, Al Gore's major thesis is that something must be done about global climate change.
In order to get to this thesis, Gore has to argue a few other things. First, he has to argue that climate change is happening. He has to argue that the world actually is warming up. Second, he has to argue that the warming is caused by the actions of human beings. In other words, he has to argue that it is not simply a natural process. Finally, he has to argue that the warming is a problem. He has to argue that this is something that can hurt the Earth and its people.
By arguing these things, he is proving (or attempting to prove, depending on your point of view) him major thesis -- the idea that something must be done about global climate change.