Setgid
From FreeBSDwiki
setgid (and it's brothers, setuid and seteuid) are all system calls that a program can use to change the group ID, user ID and effective user ID (respectively.)
From the man page for setuid:
The setuid() system call sets the real and effective user IDs and the saved set-user-ID of the current process to the specified value. The setuid() system call is permitted if the specified ID is equal to the real user ID or the effective user ID of the process, or if the effective user ID is that of the super user. The setgid() system call sets the real and effective group IDs and the saved set-group-ID of the current process to the specified value. The setgid() system call is permitted if the specified ID is equal to the real group ID or the effective group ID of the process, or if the effec- tive user ID is that of the super user. The seteuid() system call (setegid()) sets the effective user ID (group ID) of the current process. The effective user ID may be set to the value of the real user ID or the saved set-user-ID (see intro(2) and execve(2)); in this way, the effective user ID of a set-user-ID exe- cutable may be toggled by switching to the real user ID, then re-enabled by reverting to the set-user-ID value. Similarly, the effective group ID may be set to the value of the real group ID or the saved set-group-ID.