The root sense of to mean is ‘to have in mind as a purpose or intention’ (OED). The word thus denotes an impulse within the psyche, which may or may not be awarely conceptual, or expressible in language.
As a cognitive species, where few of our behaviour patterns are ‘hard-wired’, what we mean to do is central to our life’s purpose as individuals and the maintenance of harmonious relationships within a paradoxical world.
Middle English mēnen, from Old English mænan ‘intend, plan; signify’, from Proto-West Germanic *menjojanan, from PIE base *mei-no- ‘opinion, intention’, perhaps from PIE base *men-¹ ‘to think’.