""Homelab is becoming a thing even for people who never had experience with computer, people hosting their own documents, movies, music, backups in case things go bad."

Does the term "hosting" come from "web hosting" or some earlier terminology

Does the term "hosting" in the "homelab" context mean storing data locally on own computers, or running locally stored programs

If yes, could the the term "storing" be used instead

If no, then why is "hosting" the term used

This is sort of rhetorical question. I think I know why but I'm looking for clarification

Well, we're talking about network services. Which run on a host machine.

Not entirely unlike how viruses (or memes) execute on a host organism ;-)