By it's own power most likely. USB does provide power but it's not a great amount and alot of devices need more power than the USB can provide.
It depends on what type it is, if it's a hard drive type then the power will be using the battery. Some like the ipod can be charged via USB but if you playing or transfering it will be using battery power.
Most mp3 players use batteries of either 1.2v, 3.7v (iPod) or 4.2v. A USB port has a nominal supply of 5v, thus giving enough power to operate your device.