What is the 'Apple TV app Library'? Is that something I find on my MacBook?
Yes. If your Mac is running macOS Catalina 10.15 or later, then that would have the TV app. And the database of videos that are added to that app, is called this app’s Library. If your Mac is running macOS Mojave 10.14 or earlier, then that would have the iTunes application. And the database of videos that are added to that app, is called this app’s Library.
To add videos, use the app’s File menu, then Add to Library,
or else select the Library then use drag-and-drop to add a video file to its Library.
Use Home Sharing to share media from a computer to other devices - Apple Support
Set up media sharing and Home Sharing on Mac - Apple Support
Apple TV app user guide for Mac - Apple Support
Import media on your Mac into the Apple TV app - Apple Support