Administrators (or Sysops which is short of “System Operators”) are users who have been editing explain xkcd for a while and garnered the trust of the community, thus being granted tools to perform maintenance work which aren't handed to all editors due to their potentially destructive or disruptive effects. These include the ability to delete pages, block users, etc.
A full list of tasks that admins can perform can be found at Special:ListGroupRights#sysop.
To contact the admins, please post a message to the Admin requests board.
The list of all current administrators can be found at Special:ListUsers/sysop. Currently there are 13 of them.