The APEX (scalable dynamics) framework is part of the PhysX SDK (software development kit), developed by NVIDIA. 
APEX Destruction (APEX D) is a module of APEX, which is used to create destructible assets for the game environment. 
The APEX framework is available for multiple platforms, and is readily integrated into the UnrealEngine. It is free to download, provided one signs up for the NVIDIA Registered Developer Program (RDP). 
You can read more about APEX, and APEX D, by clicking on the links below: 

• APEX - NVIDIA Developer Zone  
  
• APEX Destruction - PhysX Wiki
• UDN - APEX Destruction in UE3  

It can be rather expensive, (resource intensive), to create dynamic destruction from scratch within a game, i.e. breaking a single mesh into multiple meshes in real-time, within the game engine,  while in the same instance, applying physics to those multiple meshes. 
Hence, many game developers, (past and present), utilise pre-fractured meshes/objects for their destructible objects in game. This method of implementing destruction within a game is a lot less expensive, and allows games to run on low spec platforms, as well as high-end machines. 
There are many tools on the market to enable developers to create pre-fractured destructible objects for their games. 
Some of these tools are stand-alone software packages, such as Havok's suite of physics solutions, which include Havok Destruction. These packages can be integrated into just about any pipeline, and used with multiple game engines/platforms.
Other destruction tools take the form of plug-ins/add-ons, (or scripts), that can be used within a modeling package, (e.g. Maya, 3DS Max, Blender), or a game engine, (Unity, CryEngine, UDK). Some of these plug-ins/tools are readily available with the parent software, such as the APEX fracture tool in UDK, or the shatter tool available in Maya.

Other add-ons have been created by third party companies/individuals, and must be purchased for commercial use. 
For example, Unity has a number of destruction plug-ins/scripts that can be bought through the Unity Asset Store, like the Ultimate Fracturing & Destruction editor extension for Unity 3D.  

Maya also has plug-ins/scripts, which can be purchased from third parties. One example is Ninja Fracture, part of the Ninja Dojo suite of tools.

These priced applications usually have additional features, and can allow developers to do more with their destructible assets than just simple fragmentation of meshes. 

Found some valuable info on the UDN page that covers how to create a fractured asset from a static mesh, for use in a game being made in UDK/UE2/UE3. To go to the link, click here.

I also found a cool little article, on GamerNode, which discusses the history of destruction in videogames over the past few decades. Check it out here.