Sprint is now pushing the Android 5.1 update out for the Moto X 2013. The update, which carries the software version LPA23.12-39.10, began pushing a few days ago, with more users now seeing the notification for it. As for the changes, you are getting Android 5.1 Lollipop, with its Material Design, notification enhancements and other usual goodies, as well as a patch for the Stagefright exploit.
The update should show on your phone, but if you've yet to already receive it you can manually check for it. All you have to do is head into the Settings, then about phone and check for update. If you've already received the update, be sure to let us know in the comments how its treating you.
Source: Sprint, Thanks for the tip, Caleb!