Hi,
I rigged a bird wing using vertex groups, it looks like that:
But when I rotate the the first bone, the mesh looks like this:
So why doesn’t the geometry follow it’s bones properly?
Thanks in advance!
It looks like that area is getting influence from some other part of the armature. That or you haven’t applied the scale of your bird object.
To be sure, we should know how you set up your vertex groups. Chances are you’ve done something wrong in there.
And how did you apply the armature to the mesh?
OK, while checking the groups I found it: I had the whole mesh assigned to the “main” bone, which is not needed because all the other bones are already parented to it.
Thanks a ton for your replies! 
Weight Paint!
It will fix your problem
When you’re making your armature, take some extra time to figure out which bones don’t need to deform the mesh. Uncheck Deform on all of those before parenting your armature, and you won’t need to rely on manually weight painting away those extra influences.