Being in beta status, the features of OS X Yosemite are subject to change; however, one detail that may be exciting to those who use Apple’s Messages program is the ability to both mute specific conversations, and also request or grant screen sharing access from a current conversation.
Apple’s Messages service is its attempt to merge SMS texting with classic instant messaging, and while this service started on the iPhone, Apple eventually used it to replace AIM and other messaging protocols in iChat, and bring the Mac in-line with iOS in its use of this technology.
While Messages can be used to quickly send a message using a contact’s e-mail or phone number, it also can be used to initiate FaceTime and FaceTime audio calls, and start screen sharing sessions with buddies. This last feature can often be convenient, especially when helping a friend troubleshoot aspects of his or her Mac; however, to access it you will need to choose the option for this in the Buddies menu, or by right-clicking a contact in your Buddies list.

The new options for muting a conversation or sharing a screen with your contact, are available by clicking the Details link at the top of your current conversation.
While a small change, this may make screen sharing a touch easier to access for those who regularly use it.
While Screen Sharing has its conveniences, one of the more pertinent additions to Messages in Yosemite is the ability to mute specific conversations. In Mavericks and earlier, you can switch on Do Not Disturb in Notification Center, but this will disable notifications for all applications, and not just for iChat. In addition, you can choose the option to be offline or invisible in the Messages menu, but again this will apply to all of your contacts and current conversations, and not to only one in particular.
With this new feature in Yosemite, you will now be able to continue conversations you prefer, and receive notifications for them, while preventing other people from bothering you. This can be convenient for keeping one person from badgering you and filling your screen with notices and alerts when you chat with others.