"Xposed" is a framework giving its modules deeper access to the system, by replacing some system files and so "exposing" additional interfaces.
On its main thread @ XDA-Developers, the dev introduces the framework like this:
I extended the /system/bin/app_process executable to load a JAR file on startup. The classes of this file will sit in every process (including the one for system services) and can act with their powers. And even more: I have implemented something that allows developers to replace any method in any class (may it be in the framework, systemui or a custom app). This makes Xposed very powerful. You can change parameters for the method call, modify the return value or skip the call to the method completely - it's all up to you! Also replacing or adding resources is easy.
Xposed provides a "central interface" to install so-called "modules". The latter can make use of the system calls the main app "exposed", and their name meanwhile is Legion. Many useful modules are available to enhance privacy/security, or to customize the look-and-feel, just to name the most famous areas. Some of its best known modules include:
- XPrivacy to give you control over permissions used by/available to apps; not recommended with Android 7+ due to API changes causing issues
- AppOpsXposed to give back access to the AppOps settings in Android 4.4.2
- Wanam Kit, including many useful features
- BootManager to control which apps should auto-start
These are just 4 out of ~1k mods listed in the mentioned database.