Does local mode works on faces in edit mode? I tried to move a face of a cylinder on local mode on the X axis but the orientation doesn't change no mater what I try. I really wish I could put a picture in here to show what I mean.
Local space is relative to the trasforms that you do in Object mode.
By default an objcts local space is identical to the global space. Only when you transform your object in Object mode do you edit that objects local space.
So in a way, you define the local space of an object by transforming it in Object Mode and when you enter Edit mode on that object, it's as if you are freezing it's local space to it's current state. You can then chose between the local space you've defined in Object mode or the default global space to work on your object in edit mode.
