Skype by default saves all your historical chat (IM) messages on a local computer. This can be disabled in Tools > Settings > IM & SMS > IM Settings

If you are planning to re-install Windows or migrate to another PC you may want to keep your historical chat messages. This can be done by transferring a single file from the old PC

• Close Skype on both machines
• On old PC: navigate to C:\Users\<user_name>\AppData\Roaming\Skype\<skype_profile_name> and save file main.db
  AppData folder is hidden by default.  To show hidden folders open Folder Options > View and select Show hidden files, folders and drives.
• Old new PC: navigate to the same location C:\Users\<user_name>\AppData\Roaming\Skype\<skype_profile_name> rename main.db to main.db.backup (in case you need to recover it later) and copy main.db you previously saved from the old PC.
  
• Start Skype the new PC and make sure that your old chat history is present.

Windows 7
Skype 5