Permalinks are used to make album urls nicer. When a album has a permalink defined, the id of the album is not required anymore in the url.
When a permalink is deleted, you can save it in the permalink history, so that external links to Piwigo pages still work. In the permalink history table you can see the date when the permalink has been deleted, the last time it was used and the number of times this permalink has been used.
Note that permalinks must be unique per album. Also in the permalink history you cannot have the same permalink defined more than once.