When you delete a conversation, all the messages in the conversation are deleted, and it's removed from the sidebar and your history. The conversation will be deleted from Skype on that specific device, but will still be visible on other devices unless you delete it from there too.
Find the conversation you want to delete...
- on Android: Tap and hold the conversation, tap the trash icon, then select Delete.
- on iOS: Select the chat header at the top of the screen and in the chat options, tap Delete chat.
- on Mac: Ctrl-click the conversation in the sidebar and select Delete Conversation...
- on Web: Right-click the conversation, select Delete conversation, then select Delete in the confirmation box.
Deleting a conversation is not currently supported on Skype for Windows desktop, or Skype Preview for Windows 10.