A process which can set its effective user to super-user (root). That is, although any user can run the process, the process can then execute operations which require root privileges. One example of a setuid process is the ArcStorm wservice process.
Unix terms, which are short for "Set User ID" and "Set Group ID", respectively. setuid (also sometimes referred to as "suid") and setgid are access right flags that can be assigned to files and directories on a Unix based operating system. They are mostly used to allow users on a computer system to execute binary executables with temporarily elevated privileges in order to perform a specific task.