To put it simply: A motherliness demanded or felt from a younger girl.
Originally “motherliness” is used for older women (in japanese ofc, in english it’s basically free of age), but it can also be related to younger women, and babumi is used for exactly those younger than you. From the word バブー (Babuu), a baby sound, and み is added to it, similar to 旨み (umami).
A word untranslatable into english, because of Japanese grammar and pop culture. And so I’m explaining it here. >_>