Answer: It explains what “all men” means and what it includes.
To make an "appeal to logos" means to explain something logically. It convinces the audience by using logical arguments and reason. For example, it can mean citing facts, statistics, or historical evidence on a particular subject.
In this case, King is making an appeal to logos by giving us an explanation of what "all men" means and what it includes. He hopes that by analyzing this argument, we will realize that this inclusive usage points to the universalism of the dream.