CleanLinks protects your private life (and accelerates some pages loading), by automatically detecting and skipping redirect pages, that track you on your way to the link you really wanted.
Tracking parameters (e.g. utm_*, or fbclid) are also removed from URLs.
CleanLinks also adds a “Copy clean link” menu item to the context (right-button) menu, to clean links before copying them to the clipboard.
For maximum privacy, rules are maintained and editable locally (with decent defaults distributed in the add-on). CleanLinks maintains an easily accessible history of links clean, for users to tweak the rules.
CleanLinks differs from a number of other add-ons that do parameter removal (such as Neat URL), skip redirects (such as Skip Redirect), or both (such as ClearUrls), as it automatically detects embedded URLs in the links of redirect pages.
While this means that CleanLinks offers better privacy protection, it also will break some websites that use legitimate redirects (though it tries to automatically detect most of them, such as login pages), and users will need to manually whitelist these URLs for them to work. This can be done easily via the menu from the CleanLinks icon.
Fair warning: the add-on has a bit of a learning curve, because most valid use cases vary a lot by user and thus require manual whitelisting!