Just like the other IM Chat clients, Skype is also keeping up the logs for all of your calls and chats. It records every voice calls, video calls, conversations, sms and file transfers.
All of the details are available at a click away from you, i.e. the Show History Link Button.
Here’s the method for doing it,
Just launch skype and then visit Tools > Options.
Choose the Privacy tab from left menu. Now look for the Clear History, as displayed below.
And click on Clear History.
An alert box will confirm deleting and all the history present in skype (on your computer system) will be deleted.