A program is passed a set of ``open file descriptors'', that is, pre-opened files. A setuid/setgid program must deal with the fact that the user gets to select what files are open and to what (within their permission limits). A setuid/setgid program must not assume that opening a new file will always open into a fixed file descriptor id, or that the open will succeed at all. It must also not assume that standard input (stdin), standard output (stdout), and standard error (stderr) refer to a terminal or are even open.
The rationale behind this is easy; since an attacker can open or close a file descriptor before starting the program, the attacker could create an unexpected situation. If the attacker closes the standard output, when the program opens the next file it will be opened as though it were standard output, and then it will send all standard output to that file as well. Some C libraries will automatically open stdin, stdout, and stderr if they aren't already open (to /dev/null), but this isn't true on all Unix-like systems. Also, these libraries can't be completely depended on; for example, on some systems it's possible to create a race condition that causes this automatic opening to fail (and still run the program).