Why when I apply my armature modifier the mesh won't move anymore with the bones? Let me explain in details what append:
I have made a model and I have applied an armature to it.

As you can see when in pose mode the mesh can be moved.


But when I click on the Apply button the the Armature modifier.
the mesh won't move anymore.


Is someone can help me about that ?

Thanks.
You can't apply the armature. Armature is part of "deform modifiers", when you apply this modifier the deformation gets permanent, and gets rigid. If you can't roll back (ctrl+Z, backed up file or similar) you will have to rigify your model again.