How to delete Skype history?
Go to Settings - Apps, find Skype in list of installed apps and click on clear data button and clear cache. 


  Also I need some explanations about the cases where history was resurrecting. For example, this can be because parallel client was holding history...


Skype archives your chats for you and stores them locally on your computer (or device), if you have enabled this option. Chat histories are not stored anywhere on the Skype network. source