To give someone the cold shoulder is to deliberately ignore them, treat them distantly, or make clear through manner and behaviour that they are unwelcome. The cold shoulder is not a neutral absence of warmth but an active choice to withhold it. A former friend who walks past without speaking is giving you the cold shoulder. A party host who fails to introduce a guest to others is giving them the cold shoulder.
The most widely cited origin involves Scottish or English hospitality. A welcome guest would be served a hot meal; an overstaying or unwelcome guest would be pointedly served a cold shoulder of mutton — a much inferior cut, and cold besides. The physical serving of a cold, cheap piece of meat communicated, without words, that the host considered it time for the guest to leave. Walter Scott used the phrase in his 1816 novel The Antiquary.
Scholars have noted that the food-based explanation, though appealing, has not been confirmed by pre-literary sources. Some suggest the phrase may simply use the image of literally turning a shoulder (the physical act of turning away from someone) with the emotional coldness it would communicate. Regardless of the precise origin, Walter Scott's use established the phrase in English, and his immense readership spread it rapidly.
It often is — the cold shoulder communicates displeasure through absence of action rather than direct confrontation. It is one of the most recognisable forms of social punishment in human behaviour.
The cold shoulder is deliberate. A shy person may be quiet and withdrawn but does not intend the behaviour as a message. The cold shoulder communicates a specific social message: you are not welcome, not forgiven, or not liked. Intent is the distinguishing factor.