In @eliotberriot’s words:
It’s the number of follows emitted by the account or domain that target one of your instance library
The “Emitted Library Follows” string is found under
Moderation > Domains and
Moderation > Accounts in the front-end, along with “Known Accounts”, “Emitted Messages”, and “Received Library Follows”. It essentially means “this account or domain has this many follows on your instance”.
For example, I run an instance and my user follows Eliot’s free music library on open.audio. Therefore, when I look at open.audio in Moderation, the instance has 1 “Received Library Follow” (my user following 1 library). If Eliot were to follow a library on my instance, it would show 1 “Emitted Library Follow” under moderation.
I think the string would benefit from a context clue for translation purposes.