Overview
Xposed is a framework for modules that can change the behavior of the system and apps without touching any APKs. That's great because it means that modules can work for different versions and even ROMs without any changes (as long as the original code was not changed too much). It's also easy to undo. As all changes are done in the memory, you just need to deactivate the module and reboot to get your original system back. There are many other advantages, but here is just one more: Multiple modules can do changes to the same part of the system or app. With modified APKs, you to decide for one. No way to combine them, unless the author builds multiple APKs with different combinations.
For a quick start, have a look at XDA's "Android Basics 101" on Xposed: http://www.youtube.com/watch?v=uRR0Flqx9M8
Main Features
It basically has same features as Cydia, in Xposed you can download modules ("tweaks") that can change appearances add features etc.
example: In Xposed you enable Lucky Patcher which then improves and gives you a higher chance of free in-app purchases.
Some technical details:
Advantages:
Installation:
In case of a bootloop:
Warning
This only works with root access on Android 4.0.3 up to Android 4.4. Have a look at the support thread for instructions and FAQs.
For Xposed compatible with Lolipop/Marshmallow(5.0/5.1/6.0) and tutorial use the 3rd link below
Downloads:
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Note I did not make this tool I only compiled some of the most important information about Xposed.