Unreal Engine
Unreal Engine is the game engine used to power Unreal, Return to Na Pali, and Unreal Tournament, as well as other non-Unreal titles. The unreal engine contains the backbone code which is used by the game to draw the graphics, power the UnrealScript scripting language, and all the other behind-the-scenes stuff that makes the game tick. The Engine has since gone through a number of iterations, each adding support for new technologies and features, but the basics of the engine haven't changed much since then- For instance, the same methods for making a map using the Unreal Editor remain mostly the same to the point where you can technically make a map exactly the same way on later versions of the engine as the first one (Unreal Engine 3 no longer allows plain textures to be applied to geometry- it has to be made into a "material" first- but other than this, the map building concepts remain mostly the same.) The Unreal Engine would go on to go through multiple generations- Unreal Engine 2 (used by UT2003/4); Unreal Engine "2.5", used by several licensees on multiple platforms, including such titles as Red Steel for the Nintendo Wii; and the current engine iteration is Unreal Engine 3 which powers many titles on PC, the XBOX 360, and the Playstation 3. A specialized version is also supposedly being worked on by a third party for the Wii.
See Also
Unreal Wiki- The Unreal Engine Documentation Site - This site is a valuable resource for mod-makers working with Unreal Engine 1 and 2. Descriptions of nearly every core Unreal actor (an "Actor" is basically any kind of functional object in a game map that is not geometry) and tips for modders and mappers are available here.