A modification, often abbreviated to mod, is an alteration or creation of files for a game engine, which allow it to change the gameplay style, graphics, environments, models, etc.
Types of Mods
Mods typically fall into one or more of these three categories: singleplayer, multiplayer, or TC (total conversion).
Single Player: A mod made to tell an original story, or to expand upon an existing one.
Multiplayer: A mod made to facilitate online play, against other players who also have the mod. However, since Counter Strike came out, the quality of these mods have been declining somewhat.
Total Conversion: A mod that either changes or completely rewrites the game mechanics, resulting in a game far different from what it originally was. They typically use new models, new animations, and new code, among other things. They tend to be few and far between because of the work involved, and often fall apart due to internal problems or loss of interest. (The other mod types often suffer this same fate as well.)