As the name suggests, a mod is “modifying” the game, in ways that the original creators never intended to support. That’s why out of very few exceptions (such as Paradox and Steam mods), there is not a centralized hub maintained by the creator to organize and apply mods.

The process tends to be different for every game because every game is made differently. To boil the concept down, basically if there’s no official interface for custom functionality (such as a plugin system), then modders will usually “hack” this in themselves. Installing the mod often means replacing a game file with one that hooks into the game, to be able to load custom code and custom game resources.