What do the Protestant Reformers Mean by "Total Depravity"?

  "Total" doesn't mean "utter."  It doesn't mean that we are as bad as we can possibly be.  The Reformers admit that there is much that fallen humankind can do, and can do superbly well: science, mathematics, government, art, music, painting ("culture" in general), and what Calvin calls "mechanical" arts (i.e., engineering.)

  However, "total depravity" does mean
[1]  the scope of the fall is total: there is no human undertaking that isn't fallen, sin-riddled, corrupted.

[2]  the penetration of the fall is comprehensive: there is no aspect of the human being (reason, will, affect) that is unaffected and by which we can restore ourselves. 
        E.g. (i), we can still reason (or else we shouldn't be human; the structure of reason survives the fall), but now our reason subserves the wrong end or purpose, particularly as we approach the specifically human or divine.  Reason now applies itself to aggrandizement of ourselves, or exploitation of others, or the legitimization of unconscious motivation (i.e., rationalization).
        E.g. (ii), we can still will (to be without will is to have ceased to be human), and can still will moral good, but we cannot will the good: the kingdom of God .  We cannot will ourselves out of our sinnership, cannot will ourselves into the kingdom.  (Note John 3:3: apart from Spirit-regeneration we cannot so much as see the kingdom, much less enter it.)  The will is "bound" or "enslaved" (not free) in that it cannot will righteousness.  But such bondage is never to be confused with philosophical determinism: the Reformers never say that genuine choice is denied us with respect to creaturely matters.
        E.g. (iii), we can still love, but now our affections are misaligned; we love what we ought to hate and hate what we ought to love.  At the very least we love the creature above the Creator; our loves are "disordered affections": lesser loves (legitimate in themselves) usurp our greater love (for God.)  In addition our creaturely loves are riddled with self-interest.

[3]  No one part of the society can save the rest.  The individual cannot save the society as a whole, or the society the individual.  Economics cannot put right what sociologists identify as the human problem; neither can sociologists put right what economists identify as the human problem.
    While Marx reduces all considerations (Freud's explanation included) to the dialectical laws of materialism (and one's place in the economic spectrum), and while Freud reduces all considerations (Marx's explanation included) to intra-psychic unconscious conflict, the doctrine of Total Depravity exposes both as one-sided and short-sighted.

   Note too that culture, however sophisticated (Kulturprotestantismus) is not the kingdom, is not even the vestibule to the kingdom, at the same time that culture remains a creaturely good, albeit fallen.

Wesley insisted that he differed "not a hair's breadth" from the Reformers on this point.