A Proofreader is someone who has at a minimum, the basic grasp of the written word. What that means is you have an understanding about grammar, punctuation and sentence structure. You know the difference between they're, there, and their.
A Proofreader is kind of like an editor. But, they are mostly there to read through the book and look for subplots that go unresolved, secondary characters that are introduced but then never mentioned again, glaring plot holes, inaccuracies pertaining to scenes or characters and the overall general 'feel' of the book.
To address the inaccuracies pertaining to a scene. If there is a scene where some characters are say in a truck but then the next time we go to them they're in something else. That's a hole that needs to be addressed. If a character is described one way then described another, yep, another hole that needs to be addressed. As an example, if a character is described to have black, shoulder length hair and then the next scene they have a different color or a buzz cut, that's a big hole that needs to be addressed.
Don't forget rabbit holes inside the main plot. If its not mentioned previously, that's a big oops on the author's part.
As you can see, a Proofreader is one who analyzes the story for the those pesky little macguffins that tend to pop up.