From what I understand it's a term used to describe anarchists who don't link their opposition to hierarchal authority (which can as limited as just opposing the state, as extensive as opposing all hierarchy, or anywhere in between) to a political or revolutionary strategy. That's the broadest meaning of the term afaik, and it's definitely not a cohesive or consolidated school of thought.
When I've encountered it, it's usually been used to refer to one or both of two groups of historical figures: those who espoused anarchist-like views, eg. Gandhi, Tolstoy, Tolkien, but didn't have any tangible connection to contemporary anarchist culture or activity; and those whose ideas influenced the anarchist tradition but who were writing before anarchism really became a thing, or right as it was becoming a thing (when it was incredibly nebulous), eg Godwin, Proudhon, Charles Fourier, Herbert Spencer, Thoreau etc.
Individuals in the second group are sometimes labelled as 'proto-anarchists', and those in the first group often held views that pulled in the opposite direction to the core principles of what is traditionally understood as anarchism, for example Gandhi didn't have much of a problem with the caste system and Tolstoy was a Christian (which was the source of many of his anarchist-like ideas).
It's worth noting that the broad definition I offered at the start can include many more anarchists than are covered by the two groupings (some egoist-influenced anarchists and some nihilist anarchists spring to mind), but these anarchists tend to either identify as something other than 'philosophical anarchists' (like me) or simply as anarchists, because 'adjective-anarchist' usually implies allegiance to a political/revolutionary strategy and/or to a specific prescriptive vision of society.
