What is the purpose of usb0 ethernet device on Centos 6.5 machine?

Basically, it's for TCP/IP communications over USB. Why you would want to do this varies, but usually it's because a specific device requires it. Some notable examples are the BeagleBone, USB tethering with modern Linux kernel based phones, and possibly some amateur radio devices utilizing USB (likely for packet radio).

To the best of my knowledge, usb0 is enabled and configured automatically on many Linux distros.