The woman has a strange derangement of the nervous system, having its source in the mind rather than in the body. Her stooped condition results at least partially from psychological instability, making her depressed. Her strange malady, then, is partly physical and partly mental. Satan has had his hand in her disability to the extent that her mind is susceptible to his influence, and her body has malfunctioned, producing a severe case of an unhealthy, hunched condition.
Jesus' words in verse 16, “whom Satan has bound,” do not mean that Satan's involvement here is demon-possession but more like demon-oppression. Luke does not indicate that Christ exorcised a demon from her, which would have been the case had she been possessed. Satan oppresses her in a way that affects her physical body, like Paul, who describes his affliction as “the messenger of Satan to buffet me” (II Corinthians 12:7).
God's people in every age—Job, for instance—have been aware of this work of Satan. “Whom Satan has bound” reminds us that Satan does not free anyone; he only enslaves. Not only does Satan bow people down, but so do sin (Psalm 38:6), sorrow (Psalm 42:5), and suffering (Psalm 44:25). Only God can set a person free. While creating the illusion that breaking God's law liberates, sin and Satan never truly free anyone (John 8:34). In reality, evil habits grip people with terrible tenacity. Unbelievers sometimes criticize believers, saying that their church and religious convictions restrict their fun and freedom, but such an argument is the exact opposite of the truth.