If you drive into someone's fence, you’ll probably be held liable — legally responsible — for fixing it. Liable can also mean “likely,” usually with something unpleasant: "If you don't brush your teeth, they're liable to fall out."
When liable refers to legal responsibility, it's used with "for": "You're liable for the court costs" (meaning you have to pay them). When liable means "likely," it's with "to": "If you build your house on that cliff, it's liable to fall into the river," or "That part of town is liable to mudslides." Don't confuse liable with libel, which is a legal term for slander, or saying something false and damaging about someone.
adj subject to legal action
(of persons) not exempt from an obligation or liability