Yep, it's a new feature of XenForo 2 - it is a way to let your phone or PC be alerted to notifications directly, rather than relying on e-mails. I don't use it myself, but it could be very handy for members that want to get notified immediately when they get a PM/Reply/etc... (can be configured per setting
here).
I don't find these notifications that useful myself, so I just clicked on cross (far right of bar) and then select "never ask again" when prompted.