The doctrine that fallen man is completely touched by sin and that he is completely a sinner. He is not as bad as he could be, but in all areas of his being, body, soul, spirit, mind, emotions, etc., he is touched by sin. In that sense he is totally depraved. Because man is depraved, nothing good can come out of him (Rom. 3:10-12) and God must account the righteousness of Christ to him. This righteousness is obtainable only through faith in Christ and what He did on the cross.
Total depravity is generally believed by the Calvinist groups and rejected by the Arminian groups.