IPA: /ˌæd.mɪ.nɪˈstreɪ.tɪks/
KK: /ədˌmɪnɪˈstreɪtɪks/
A woman who manages or oversees an organization, project, or estate.
The administratrix was responsible for overseeing the distribution of the estate's assets.
Administratrix is formed from "administrare" (meaning to manage or direct) and the suffix "-trix" (meaning a female agent). The word refers to a female who manages or directs affairs.
Think of a woman who is 'managing' ('administrare') something — that's what an administratrix does.