What is AppSync

First, meet installd.

installd is part of iPhone OS/firmware, his location is /usr/libexec/installd. It’s managing the installation and compression of apps on your iDevice.

Here is the process while you are syncing & installing an app to your iDevice.

And here is the process while you are syncing & copying an app from your iDevice.

See the blue boxes in both pictures, it shows that the processes fail.
That’s what happens when you try to install/sync c-r-a-c-k-e-d a.k.a jailbroken apps using the original installd.

And then, AppySync exist.
AppSync is a system tweak. When you install AppSync from Cydia, AppSync creates backup of installd by renaming installd to installd.backup, and invites a tenant to live in place of the original installd. This new installed installd works just like the original except that it totally skips the blue boxes, so the processes don’t fail anymore, no more DRM checks, all apps will be passed and installed without any interruption.

By installing AppSync, you are simply patching installd. It doesn’t affect (installation and syncing of) your legitimate apps from iTunes store.

It’s a bit explanation of AppSync.

*Illustration source: hackulous forum