Hi Salvater. You did not seem to understand the definition, nor Gary's explanation. Seeing Gary seldom gives follow up answers, I'd like to offer a few lines.
Quotation(except for the words in the square brackets):
1Expressing the relationship between a part and a whole.
1.1With the word denoting the part functioning as the head of the phrase.
‘the sleeve of his coat’[the word: sleeve]
‘in the back of the car’[the word: back]
‘the days of the week’[the word: days] (unquote)
The prepositional phrase "with the word......head of the phrase" serves as an adverbial to the clause " (of) expressing the relarionship ....... a whole", and the clause following "with", namely " the word denoting the part functioning as the head of the phrase" is an absolute construction( some interpret the whole construction "with......whole" as an absolute construcrion, though) ，which has its logical subject ("the word...") and logical predicate("functioning as...").
I bet you know about the concept "absolute construction". You merely forgot it at the time you read the definition, hence the confusion.