# Wording of a group action

My textbook says the following: "Let ##G## be a group and ##G## act on itself by left conjugation, so each ##g \in G## maps ##G## to ##G## by ##x \mapsto gxg^{-1}##". I am confused by the wording of this. ##g## itself is not a function, so how does it map anything at all? I am assuming this is supposed to mean that ##g \cdot x = gxg^{-1}## is the definition of the action, but why does it use the map notation as if ##g## is a function, when ##g## is really an element?