Published label: shall appear on your store front. Un-Published label: shall not appear on your store front.After you create a label on your shop, the label is in published state.
Steps to change state a label :
Step 1 :On back end go to app' dashboard >> Product Label >> Click Shop Lables on the left menu to see all labels on your shop.
Step 2 : To change publish to un-publish state, mouse click on the Published Icon:
A label could be in 2 states: Published 
or Un-Published 
Please wait a message notify that process is successful and the icon state is changed.
To change change un-publish to publish state, please do the same.