Add-ons are extra payments on top of a base transfer fee, triggered only if agreed conditions happen: a number of appearances, goals, international caps, a trophy or qualification for European competition. They let a buying club pay less up front and a selling club share in the player succeeding.
They exist because the two clubs disagree about the player and neither will move. The buyer thinks the asking price assumes a level the player has not reached; the seller thinks the offer ignores what the player will become. Add-ons settle the argument by making part of the fee conditional on who was right.
How reachable the conditions are varies enormously, and this is where reported fees mislead. A headline that quotes the base fee plus every add-on describes a maximum that may need the player to become a regular international and win a trophy. Only the guaranteed part is certain to be paid.
Some triggers depend on the club rather than the player, such as qualifying for the Champions League, so a selling club can end up receiving money because of a season it had no part in.