"Substrate 0.9.5000 has been released, with support for iOS 7 and ARM64. (For extensions to work on ARM64, they must be recompiled to ARM64.)"
The update means most tweaks can now work properly on all devices! You can get Substrate 0.9.5000 from the Changes tab in Cydia. It make take some time for developers to recompile their extensions for the 64-bit processor so keep checking back or follow us with the links below.
Cydia Substrate supports frameworks used by iPhone projects such as WinterBoard, Activator, and Five Icon Dock. The general idea is that there are a number of reasons one might want to hook functionality into an existing application. In order to do this there are a few dangerous or complex steps. By cnetralizing the code for these we can hope to get them right. As an example, MobileSubstrate provides a simple platform (one integrated with Cydia) for deploying code that gets inserted into graphical applications. When things fail, it as able to provide error handling and fallback support (think of a "Safe Mode").