The first two are somewhat self-explanatory; it has been suggested that the third is deliberately somewhat vague. The doctrine thus established is called Congressional immunity; it arose out of the necessity to prevent a vengeful executive from arresting members of the legislative branch on a pretext to prevent them from taking actions that the executive might find to be displeasing. In recent years, this doctrine has been used to prevent members from being stopped and held for speeding on their way to sessions; this apparently is not a "breach of the peace", where as perhaps another misdemeanor such as "drunk and disorderly" might be construed to be such.
Most states of the United States and most other English-speaking jurisdictions have extended this privilege to members of their legislatures on the theory outlined above.
The concept of a "breach of the peace" is more widely used in English law, however. Theoretically all criminal offences cognizable by English law involve "a breach of the King's (or Queen's) Peace", and all indictments conclude "against the Peace of our Lord the King (Queen), his (her) Crown and Dignity".
Historically this phrase, now legally superfluous, represents the last trace of the process by which the royal courts assume jurisdiction over all offences, and gradually extruded the jurisdiction of the sheriff and of lords of manors and franchises, making crime a matter of national concern as distinguished from civil wrongs or infractions of the rights of local magnates. The Peace of the King was sworn on his accession or full recognition, and the jurisdiction of his courts to punish all violations of that peace was gradually asserted. The completion of this process is marked by the institution of the office of Justice of the Peace.
In the United Kingdom, although not a statutory offence but a common law offence "Breach of the Peace" is widely used In the United Kingdom, constables(anyperson power, not just Police) are also permitted to arrest a person to "Prevent a further Breach of the Peace" which allows police constables to arrest a person before a Breach of the Peace has occurred. This is permitted when a constable holds a reasonable belief that should the person remain, that they would continue with their course of conduct and that a Breach of the Peace would occur. Breach of the Peace is usually used to remove violent or potentially violent offenders from a scene rapidly; the only punishment that can be inflicted by a court for this offence is to "bind over" the offender to keep the peace. There are some minor differences between English Law and Scots Law in relation to breach of the peace.
The conclusion has also found its way into constitutional law in many United States state constitutions, which mandate that indictments within the state end in a similar manner to the above, usually omitting the "crown" part or substituting "government". For example New Jersey's is "against the peace of this State, the government and dignity of the same.