Hello Nikifor,
It is an expression used when someone is in a fit of the sulks mainly because the person was offended by something or someone.
“Faire la tête” or “faire la gueule” is similar in terms of meaning.
“Tirer” can also be used instead of “faire”.
“Il tiré une tête de six pieds de long à cause de son erreur.”
He was sulking over his mistake.
“To sulk” can be translated to “bouder” in French, and this might be a bit of a “kiddish” way of saying that someone is not happy.
I hope that helps.