Lawful Interception (LI) refers to the ability of law enforcement to eavesdrop on users of communication networks providing they have the authority to do so. It is the government's legally-sanctioned access to private communications, such as telephone conversations, e-mail messages, direct messages, and the like.
In the example of the US, the authorities citing just cause would bring a warrant to a mobile network carrier (MNC) requesting access to the channel and supporting data. If the state brings a compelling case as per law and precedent, the access would be conditionally granted.
In jurisdictions where civil rights such as the right to privacy are unevenly protected, or are not protected, the circumstances might differ markedly from the US, developed-nation, or Western European experience. Indeed a North Korean citizen may have their conversations monitored often, and the DPRK has the legal authority to do it without a warrant due to the nature of the regime. It is not a matter of judgement, it's a matter of law.
The precise methods of lawful interception have changed since the era of hardline telephones but the legal principle is the same. The interception is targeted to an individual or individuals as opposed to a broad surveillance effort that would fence in a lot of data for filtering or storage.
“In jurisdictions where there is due process and privacy is observed, something like the authorities’ lawful interception of communications is tolerated. At the other extreme are other repressive regimes where the monitoring of citizens is done rather arbitrarily and abusively. We should remember, these are ‘lawful’ instances as well but not something to which many people are accustomed.”