Offstring yoyoing is a style where the yoyo string is attached to your finger, but not to the axle of the yoyo. This allows you to launch the yoyo up in the air completely disconnected from the string, and then catch it back and wind it back up. It's tough to learn, but really impressive once you learn a few offstring tricks. Offstring yoyos are typically a little bit larger and have a flared gap shape to make them easier to catch back on the string.
Please note that you aren't required to use any of these yoyos as offstring yoyos. They also work just fine as regular yoyos, and perform classic yoyo tricks with ease.