To enforce a law simply means to ensure that the law is being followed. The definition of enforcing is to require observance of or obedience to something, of which the law is one example.
Who Enforces the Law
When referring to enforcing a law, people are usually speaking of the police. The police are granted the right to protect the law, which includes the power of force. They arrest those found breaking the law, and the criminals then face legal charges in court, where lawyers and judges carry out the law. The FBI and CIA are examples of federal agencies that also have the right to enforce the law.
How the Law is Enforced
The police are authorized to use appropriate force when encountering a person breaking the law. In America, they are equipped with mace, a baton and a gun for this purpose. Police generally withhold on using force until the threat of force from the criminal occurs. Typically, the police handcuff the person, take them down to the station for questioning and read them their Miranda rights, which let the lawbreaker know they have the right to remain silent and the right to an attorney.
Purpose of Law Enforcement
The necessity for law enforcement comes from creating the law in the first place, which seeks to establish a set of stipulated rules for society to function without crime and chaos. The purpose of law enforcement is to minimize the violation of these rules and diminish social disobedience. This process often ends in incarceration for parties that break the law, with the hope of possibly rehabilitating these parties and returning them to normal society at some later point.