What does give someone the cold shoulder mean?

It means to snub them - the mental image is turning away so that you no longer face that person.

Giving a cold shoulder to someone means that you are treating them with disdain or an unwelcome attitude. Part of that could be avoidance, but it often refers to rudeness or turning away while someone is trying to talk to you... that sort of thing. It usually has a context of the person doing it for a reason, or on purpose... a perceived slight, or because someone doesn't "merit" the other person's company, or something like that. It involves cruelty as revenge for whatever the other person is supposedly doing wrong... you couldn't give someone the cold shoulder accidentally.

If you give someone the "cold shoulder", you completely ignore them.

Giving a person the 'cold shoulder' is usually understood to mean ignoring that person in a social situation. It can more loosely refer to other situations where one ignores or barely acknowledges another person.
A "cold shoulder" is what you get when someone is deliberately avoiding you.

For Example:

"At the party she tried to tailk to him, but he gave her the cold shoulder."

To behave towards someone in a way that is not at all friendly, sometimes for reasons that this person does not understand To give someone "the cold shoulder" is to ignore them.

if you are giving some one the cold shoulder its like the silent treatment you turn away from the person and have your shoulder face them