Metaphor derived from Archimedes supposedly saying that, if he had a fulcrum and a lever, he could move the earth.
René Descartes mentions it in his second meditation:
"Archimedes, that he might transport the entire globe from the place it occupied to another, demanded only a point that was firm and immovable; so, also, I shall be entitled to entertain the highest expectations, if I am fortunate enough to discover only one thing that is certain and indubitable."
The Archimedean point is thus an external point from which a different, perchance objective or true picture of something is attainable, by removing oneself from this picture and taking an overview.
Examples: a view of time from outside of time or a view of spatial reality from nowhere.
Philosophers of a sceptical or anti-realist bent, as well as minimalists, often claim that such an alleged standpoint is solely fantastical, and the asserted objectivity of the view mythical. "We can no more separate our theories and concepts from our data and percepts than we can find a true Archimedean point - a god’s-eye view - of ourselves and our world." (Michael Shermer)