In Social25 package version 2.59 we introduced Browser Notifications for incoming chat messages. In order to use this functionality the setting needs to be enabled in the Social25 config:
This can be found in the subsection Connected App.
When enabled, this allows active chats (which are open in a Salesforce Tab) to be monitored for incoming chat messages. When a chat message is received, you will receive a generic notification in your browser that informs you that a new message has been received.
Users need to allow browser notifications from Salesforce for this functionality to work. You can check this in the website permissions of your browser.
Individual users can also choose to block browser notifications from Salesforce to disable the functionality on an individual basis.