I’m experimenting with Libre Office’s Database for the first time. The wizard asks me if I want to register it. What is that all about?
Simply check that option. It won’t harm.
Registered databases appear in the data source window, so they are accessible from Calc and Writer (even Impress and Draw, but these are highly exotic use cases).
In Calc you can link cell ranges to record sets and you can build pivot tables from record sets.
In Writer you can use mail merge fields for serial letters with registered databases.
Without registration, you can access the database by means of embedded input forms and embedded reports but not outside the Base container.
If you don’t want the registration, you can remove it at any time via Tools>Options>Base>Databases
Registration, as proposed in the situation you describe, is another word for declaring the database at a LibeOffice module-wide level (the path and name of the DB file get stored in the LO configuration file).
In short: You give the connection an additional name, to be remembered. I use it two ways:
- When I install files on different devices for different setups, I don’t need to adapt pathnames or use variable like %USERPROFILE% as I already registered my photo-database as EXIFDB.
- I have a bunch of laptops used to input data. Usually I don’t need to access this files “manually”, but just in case each of them is defined as separate datasource with different names INaa, INxx etc. So i can quickly exchange the source databases for my analytical .odb (Actually I could also do this in ODBC configuration, but having this in LibreOffice is convenient and portable.)
… like without doc or what ? 
pressing F1 you should rapidly end up to sth like : Registering and Deleting a Database