A conjunction is a word that links words in a sentence, different clauses or different sentences that are widely used in writing because they provide organization and coherence to ideas. Additionally, conjunctions can be of different types, this includes subordinating conjunction that includes words such as although, before or when that creates a subordinating or dependence relationship; coordinating conjunctions used to join elements of the same importance and correlative conjunctions that are pairs of conjunctions such as not only/but also or both/and also connect to elements with the same importance. This means the underlined conjunction in the sentence that is "Both" and "And" is one correlative conjunction as this conjunction links to elements of the same importance "Billie Holiday" and "Ella Fitzgerald" but because this conjunction is pair conjunction.
The child seems like they aren't good enough to do whatever it is the mother insists she's good at. The mother thinks highly of her child, and knows her child can do anything she wants to. But the child is just not confident.