Out of Band Management is the ability to access your network equipment remotely using a network connection other than the main one used by your organization.  You can use Out of Band Management equipment to connect to management ports on network equipment and servers to connect using everything from dial up connection to LTE.

Out of Band Management is used so that remote administrators can access equipment even if something happens to the main ISP connection.  Also it is used as a way to protect infrastructure equipment from hacking since it can be setup so that LAN users cannot connect to admin ports.