Galaxy Tab 3 owners on T-Mobile are getting a rather huge upgrade in the form of Android 4.4 KitKat, which is now rolling out to the 7-inch tablet that has been stuck on Android 4.2 ever since it launched. The update will take the tablet to the latest version of KitKat (4.4.4), and like all other updates, is making its way over the air and via Samsung Kies, with the OTA available only on a Wi-Fi connection for the initial few days. T-Mobile hasn't mentioned any special changes, but you can expect the usual KitKat features like faster performance, white status bar icons, album art on the lockscreen, and wireless printing support.
Head over to the source link for more details on the update, and also check out the Settings » About tablet » Software update menu to see if the OTA is already available for your device. Oh, and do keep in mind that this will probably be the last update that comes to the Galaxy Tab 3, as the device is neither that high-end or new to warrant an upgrade to another major iteration of Android.