Legal liability is the concept that a party has some obligation owed to another party or parties. Legal liability is imposed by the "legal system," but this is more than just the court system. For example, the state or federal government may impose liability against a party who pollutes the environment or improperly operates a drone. Most people are found to be legally liable by a judge as a part of their judgment. As judicial example, if you breach a contract, you are liable for that breach for the amount of the damage you caused another party. A party can obtain a judgment and hold someone else liable by going through the standard litigation process: file a Complaint, have a trial, and obtain damages or other relief.
It is rare, but sometimes a party can be immune from liability. It is what it sounds like: immunity. This comes in a variety of forms such as sovereign immunity, diplomatic immunity, judicial immunity, qualified immunity, or statutory immunity. A party might still be liable, but as a matter of public policy, that party is immune from judicial enforcement as a result of that liability. Two examples, 1) the government may be negligent and harm your soil, but the government has sovereign immunity; 2) you have a 4th amendment right from unreasonable searches and seizures, but police often obtain qualified immunity to provide some breathing room for them to act and make minor errors. Whether those immunity examples (or any immunity) constitute good public policy is definitely an interesting question, but for the purpose of legal liability... those who obtain immunity are "immune" from that liability.
The Peterson Legal Team offers civil litigation services to our clients. If you have a claim against a person who you believe is liable to you, please contact our office to discuss your case. Likewise, if you believe someone is immune to liability or you believe you may be entitled to immunity, we are happy to make an appointment with one of our attorneys to discuss your case.