SysOp is short for "system operator". It is a commonly used term for the administrator of a bulletin board system (BBS) or special-interest area of an online service or, historically, the operators of any computer system, especially a mainframe computer.
Usage of the term peaked in the early 1990s, being mostly used strictly to refer to BBS operators; someone doing equivalent functions on the Internet is primarily referred to as a "sysadmin", short for "system administrator".
A Co-SysOp was a user who was granted certain admin privileges on a BBS. Generally, they would help validate users and monitor discussion forums.