Papyrus scripts allow designers (and by extension, modders) very easy access to implement features important to gameplay without hard-coding those features into the executable. Traps, triggers to spawn monsters and sound events and NPC actions (and interactions), just to name a few. Papyrus (the language the scripts are written in) is rather powerful (compared to past iterations of Bethesda's scripting languages) and can facilitate complex new features and player interactivity.
See http://www.creationkit.com/category:papyrus for more information.