How does it affect the performance if an iMac 1TB internal hard drive is mirrored on an external drive? I am getting an iMac 27 inch, and it will have a 1 TB internal hard drive, and I know we can set up the Mac so that this hard drive is mirrored on an external 1 TB hard drive using the built in tools of Mac OS X (Applications -> Utilities -> Disk Utility).

But the OS's system files, the swap file, etc, are all on the internal drive as well.  Will those be mirrored as well?  If so, won't that slow the system down a lot, since the external drive is usually slower than the internal drive.

Also, even if the OS's files are not mirrored but just the user's own files, will copying or file saving be slower, since instead of copying to the faster internal drive, the OS will report done only after the external drive is done as well?
A mirrored RAID would operate only as fast as the slowest drive in the setup.  In this case, unless you are using thunderbolt I imagine the performance would be awful.  Another reason not to do a mirror with an external drive (if Disk Utility would even let you) is it'd be too easy have the mirror fail for a number of reasons.

I would use Time Machine to the external drive rather than mirroring.  Remember that RAID is NOT backup!  If you mess something up then you will lose data, a mirrored RAID is not going to save you at all.  Only Time Machine or a similar backup strategy will help prevent data loss.