A party is liable when they are held legally responsible for something. In personal injury law, liability usually goes hand in hand with negligence.
However, in “strict liability” cases, a plaintiff does not have to prove the defendant was negligent. (Example in Nebraska: Subject to a few exceptions, dog owners are automatically (strictly) liable for injuries/damages as a result of the dog’s action.)
Vicarious liability is when an additional party to a defendant is responsible. This is often the case when an employer is legally responsible for the actions of supervised employee.