A spool in the context of a database is a mechanism, meaning parts of individual components inside the database engine working together to move data in, out and around the database as required and it must do this in a logical flow.
Just like with a thread on a normal spool, if you wanted to use the thread you would have to start from where the thread starts and logically unwind the spool as it was winded into the spool. You cannot start unspooling at the end if the thread or in the middle.
A database saves each “thread” of data it received logically in that logical order. That is also how a database moves data around the place by ti goes to the storage and picks up the records it needs in the same order that they were stored.
The term can also be used when starting a new database with a backup and can be phrased spooling up a new database.