By far the best and largest source of mods is the Steam Community Workshop, which gathers, gives out, and sometimes sells player creations. Nowadays, it's thankfully much easier to install these mods: it's as simple as downloading a file and installing it.
And, for nearly as long, those edits have passed back and forth on the internet. Video game players have been mucking about on the back-end of popular titles – from 'Skyrim' to the earliest text-based adventures – for as long as games have been on the market. The mod is the house built on top of that foundation. Think of the original game as the foundation. The mod runs on top of the original game.
Some game studios create custom 'mod tools' for their games, making the process even easier for the less code-minded among us. In order to play a mod – even ones that are essentially full games – you need the underlying game on your computer. Sometimes, fans create new games altogether (we're looking at you, 'DOTA'). Savvy fans dive into the back-end of their favorite games to fix bugs, update graphics, or introduce new elements.
'Modding' is just jargon for 'modifying' – altering – video games.