In Library Manager, the History tab shows the libraries that have been loaded recently (since the last Clear or Clear All). This list is independent of any particular project.
Typically we use the exact same libraries all the time. But there are exceptions; sometimes you need the version 7 library, for example. If you've loaded that library recently, you can add it from the history tab instead of scrolling through the whole Local/LAN tree.
It's also helpful if you take projects home. When you open a project in a different location, the library manager will come up because the servers aren't there and your local Archicad folder path is different. But the history tab remembers the local instances of the libraries, making it easy to load them quickly.
If you load a "wrong" library at some point, you can use the "Clear" button to delete it from the history so you're not tempted by it in the future.