Trixie - 'finalise' is simply 'locking' the dvd disk so no more recordings can be saved to it, or the recording deleted.
It is simply done on the machine that made the recording (it won't work properly if done on a different machine) and takes a few seconds.
I don't know how it works technically but I assume it removes any codings specific to that recorder that enables deletion or more recordings to be added.
After finalising, the disk should play on most players.
On my recorder, it is simply a case of pressing a button in the options menu.