Someone who's reproachful is deeply disapproving. A reproachful look on your mom's face is a sign that you've disappointed her and might be in trouble.
When you criticize your friend's decision to borrow her parents' car without asking, you probably sound reproachful. You might not even need to speak — a reproachful glance is sometimes enough to communicate your disapproval. When you reproach someone, you express disappointment in them, and to be reproachful is to be "full of reproach." The root word is the Old French reproche, "blame, shame, or disgrace."