If you set temporary avoids, they are cleared every time you cycle power.
If you set a permanent avoid (by hitting the avoid button twice) on a frequency while listening to that freq in a favorite list, it is avoided in that favorite list, but not in the main database. For example, you create a favorite list called Police, populate it from the database, and listen only to that favorite list. You hear some non-police traffic on 123.456 and put an avoid on that freq. That avoid is stored in the Police favorite list. If you turn off the Police list and turn on the main database, you will hear traffic on 123.456 again.
If you never want to hear 123.456 again, avoid it while listening to the main database. But you still might hear traffic on it if it is a local frequency (as opposed to a nationwide, like CB or FRS), and you travel to another state where there is a different local database entry for 123.456.