If you are signed in to Skype and you receive an instant message when the conversation window is not open, a numbered badge will appear next to the contact in the sidebar. The number displayed indicates the number of unread messages in the conversation.
A red numbered badge will also appear on Skype in the dock. This indicates the number of conversations with unread messages.
If you receive a new instant message from participants during a voice or video call, you will have a red badge on the Chat button: 
Select it to read the instant message.
Learn more about sending instant messages.
