I'm not sure when the term "mod" for the modification of a game emerged. But it is quite possible that it came into use with the Diablo mods.
Diablo is an extremely moddable game. There is something unfinished about it; unused graphics lead a hidden life in the dat files, possible attributes have never been implemented. No wonder that some mods are better than the original Diablo itself.
Diablo mods are usually written for version 1.07 and are multiplayer only. They either come as dat files and require dhack, or as separate executables. Most of them were written between the releases of Hellfire and Diablo II.
Blizzard was a bit sceptical about the whole mod business at first, but they seem to have come to terms with it. Here are a few pages about mods in general:
They were the ones that started it all… They had four mods: One for the original Diablo, one for Hellfire, one for Diablo II, and the Middle Earth Mod for the original Diablo, most of them are designed for multiplayer only. There have been several interviews with Varaya and Khan:
Since most mods were created between the releases of Hellfire and Diablo II, many of them were designed for Hellfire. But since it took me so long to lay my hands on this add-on, I had never become as interested in those.
There are also several modmakers, programs that help you create your own mod. But their homepages are all gone. You can find two of them on my own mod page and some more, I think, on Judge Hype, but it's in French.
There are a number of mods for Diablo II, I have listed some of them there. Since there has been no further sequel yet, this game is still modded a lot.
