Question

My grandmother saw both billie holiday and ella fitzgerald perform.what kind of conjunction are the underlined words?

Answer 1

I'm assuming the underlined conjunctions are both and and (because you didn't underline any, and those are the only two conjunctions in the sentence).
Those conjunctions are called correlative conjunctions - this means that they are connecting two items which are equally important. So, this woman saw both Billie Holiday and Ella Fitzgerald - and both of those artists are important to the woman.