Motorola has always offered an official bootloader unlock option for the Moto X devices, but not all variants have been eligible. Specifically, AT&T and Verizon have blocked the process. Now, that's starting to change with the addition of Verizon's 2014 Moto X to the list of unlockable devices.
So, why would you want to unlock the bootloader on this phone? Well, Motorola isn't going to be offering anymore official updates for carrier versions, so an unlocked bootloader lets you install a Marshmallow ROM on the device. It's lame that Motorola isn't updating the device anymore, but at least it's giving you the option of doing it yourself. Users are getting unlock codes for this device without issue, but the AT&T variant is still claiming it isn't supported for unlocking.
Unlocking the bootloader on a Motorola device is a bit different than it is on a Nexus. You'll have to run an ADB command to get a code, put that into the Motorola online tool, and it will give you a code to input as a fastboot command that unlocks the phone. As usual, this comes with warning about potentially breaking your phone, losing data, and bringing about the end of humanity. Proceed with caution.