Babying fanfiction is basically fanfiction that focuses on a certain aspect of babying characters. It can be a way for fans to explore different dynamics. Sometimes it can be about a character who is normally strong and independent but is placed in a situation where they are vulnerable and are cared for in an excessive or endearing way. It could also be a form of wish - fulfillment for fans who want to see their beloved characters in a more tender, protected state. It often plays with the emotions of the readers and can be quite popular among certain segments of the fanfiction community.
Babying fanfiction typically involves writing fictional stories within a fanfiction context where one or more characters are treated in a 'babying' way. This could mean they are coddled, protected, or infantilized in the narrative.