This is an example of the use of a subordinate clause which is also an adverb clause, this kind of clauses provide additional information that could be either describe a noun in the main sentence or to give further information, the word that is acting as a subordinating conjunction is "While" this is adding extra information that can not be used independently from the main sentence.
This clause gives us information about when something happened, more precisely when Mrs. Bailey said this quote. From this we can see that this clause modifies the verb <em>said</em> making it an adverb; Adverbs modify verbs and adjectives modify nouns.
If we want to be even more precise, this is an adverb of time.
The answer is MacDuff, she was not "born of a woman" because he was delivered by C-section (<span>caesarean section). That was not common back in the day.</span>
