This answer is about the King's Peace in medieval Europe, but there may have been Classical predecessors and I believe in some countries in Europe there is even still a King/Queen's Peace. I'd also be very interested if historians here who work on non-European cultures could weigh in if they know of something similar.

The King's Peace was the idea that, within the realm of the king, there is supposed to be no violence, and the king guarantees that. The guarantee means that the king, or his agents, had the right to enforce the peace, either through violence to stop unauthorized violence or through retributive justice after the unauthorized violence was committed. In legal texts, it is sometimes used as a legal standard. It sometimes had an almost encompassing, geographic feel to it, and was used with prepositions like in.

The peace was often invoked in legal proceedings. Here are a couple of examples from English court records where the king's peace is being invoked:

Serlo of Ennis-Caven appeals Osbert of Dimiliock and Jordan, Walter's son, for that they in the king's peace wickedly assaulted, beat and seriously wounded him, so that by reason of the beating three bones were extracted from his head; and this he offers to prove against him under the court's award as a man maimed by that mayhem.^[1]

And the county showed him how Hugh had brought the Justiciar's letters pardoning him the flight and outlawry, and that he was to find pledges to stand to the king's peace, but had not returned. Whereupon the king's serjeant was ordered to seek Hugh and bring him to a later county [court].^[2]

Along with the King's Peace, there were several other types of Peace that were common in the Middle Ages. For example, in his book The Murder of Charles the Good^[3] Galbert of Bruges talks about two types of Peace. The first was the Count's Peace. Flanders, where Galbert lived, was technically under the French king. But since the king of France had no real political control in Flanders, it was up to the count of Flanders to maintain social order and therefore peace and justice. The other is the specific peace's that the count was supposed to declare during the annual Fair. This was a very important issue, because the Fair was the largest commercial gathering each year. Flanders had little agriculture, and relied increasingly on trade for its economy. If the peace weren't upheld, southern merchants wouldn't come to the fair to buy goods, and the producers in Flanders wouldn't be able to make money. The inability of Charles the Good's replacement to uphold the peace at the fair caused a rebellion in Flanders.

The final type of Peace is the Peace of God. There are two components to the Peace of God, one of which was practical and one of which was theological. It was very popular in the 11th century as the Millennium approached. Ideally, the Peace of God was extended over the whole world. By enlarging Christendom, Christians would enlarge the ability of the Peace to be upheld. It's as an agent of God that the King was supposed to uphold his own Peace.

The practical part you may be more familiar with. This was the idea that places and people under God's protection should be free from violence. Therefore violence in churches, against the poor, or against clerics was a breach of the Peace of God. This is where the idea of going into a church to seek sanctuary comes from. You can see a declaration of the Peace of God in this French source from 989.

That source is a good example of the popularity of the Peace in the time leading up to the Millennium. There were many other such declarations made around that time throughout Europe. The reasons for this are complicated, but a simple explanation for it is that Christians were readying themselves as much as possible for the Second Coming of Christ. If you are interested in this topic further, the historian who has worked most recently on the Peace is Richard Landes. A good starting place would be a book he wrote with Thom Head called The Peace of God: Social Violence and Religious Response in France Around the Year 1000.^[4]