For example, how are the classes "fa-square-o" and "fa-square" different from each other? Where can I find more information on font-awesome class name conventions? I searched on their website, but couldn't find specific guidance on font-awesome class naming conventions.
It means outlined. Some icons have full solid backgrounds, and some others are just outlined, and are named with an extra -o at the end of their names. Besides this, there'a also -alt, which is used for icons which are alternatives to other icons. E.g., the icon fa-arrows, has an alternative fa-arrows-alt which has a slight rotation, different from the normal icon. I guess these two are the only ones to be mentioned.