Proof of an External World is not what it proposes to be. Instead of offering proof, per say, Moore asks the reader to fill in the blanks. He suggests that the reason he believes in the objective reality of the physical material world is that he experiences it, so he asks the reader (and his thought community) to ignore ideas that are intentionally obfuscating, and instead to return to the basic facts of the observable human life.
The book was not revolutionary, but it is important in its time. Like Aristophanes "In the Clouds," the issue is that philosophers had become enamored with their own creativity and novelty, and instead of trying to talk about shared human experiences, they preferred esoteric, interesting sounding ideas.
One problem with that criticism is that it doesn't actually offer much by way of argument against those esoteric ideas. The fundamental assertion that we should trust our experiences is what de Cartes tried to disprove in his writings more than two hundred years earlier.
The reason for this dilemma is that the question is essentially unprovable. It's very important to read this in light of Wittgenstein who was also writing about ontology and epistemology (which is also the category of this Proof). Ontology is the philosophical discussion of what exists and how existence occurs, and epistemology is the analysis of the human capacity for knowledge and belief.
This is an epistemological, ontological argument toward what some might consider to be a sort of Logical Positivism, and the question of whether this document influenced Ayer and the Positivists is certainly a meaningful one.
